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Solutions of nonlinear nonhomogeneous Neumann and Dirichlet problems
1. | American Institute of Mathematical Sciences, P.O. Box 2604, Springfield, MO 65801 |
2. | Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780 |
References:
[1] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, The spectrum and an index formula for the Neumann $p$-Laplacian and multiple solutions for problems with a crossing nonlinearity, Discrete Cont Dyn Systems, 25 (2009), 431-456. |
[2] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, On a $p$-superlinear Neumann $p$-Laplacian equation, Topol. Methods Nonlin. Anal., 34 (2009), 111-130. |
[3] |
A. Allendes and A. Quaas, Multiplicity results for extremal operators through bifurcation, Discrete Cont Dyn Systems, 29 (2011), 51-65. |
[4] |
D. Arcoya and D. Ruiz, The Ambrosetti-Prodi problem for the $p$-Laplace operator, Comm. Part. Diff. Equs., 31 (2006), 849-863.
doi: 10.1080/03605300500394447. |
[5] |
V. Benci, P. D'Avenia, D. Fortunato and L. Pisani, Solitons in several space dimensions: Derrick's problem and infinitely many solutions, Arch. Rational Mech. Anal., 154 (2000), 297-324.
doi: 10.1007/s002050000101. |
[6] |
R. Benguria, H. Brezis and E. H. Lieb, The Thomas-Fermi-von Weizsäcker theory of atoms and molecules, Comm. Math. Physics, 79 (1981), 167-180.
doi: 10.1007/BF01942059. |
[7] |
H. Brezis and L. Nirenberg, $H^1$ versus $C^1$ local minimizers, CRAS Paris t., 317 (1993), 465-472. |
[8] |
S. Cano-Casanova, Coercivity of elliptic mixed boundary value problems in annulus of $\mathbbR^N$, Discrete and Continuous Dynamical Systems, 32 (2012), 3819-3839.
doi: 10.3934/dcds.2012.32.3819. |
[9] |
K. C. Chang, "Methods of Nonilnear Analysis," Springer, Berlin (2005). |
[10] |
S. Cingolani and M. Degiovanni, Nontrivial solutions for $p$-Laplacian equations with right hand side having $p$-linear growth, Comm. Part. Diff. Equas., 30 (2005), 1191-1203.
doi: 10.1080/03605300500257594. |
[11] |
S. Cingolani and G. Vannella, Critical groups computations on a class of Sobolev Banach spaces via Morse index, ann. Inst. H. Poincare-AN, 20 (2003), 271-292. |
[12] |
S. Cingolani and G. Vannella, Marino-Prodi perturbation type results and Morse indices of minimaz critical points for a class of functionals in Banach spaces, Annali di Mat. Pura Appl., 186 (2007), 155-183.
doi: 10.1007/s10231-005-0176-2. |
[13] |
P. Clement, M.Garcia Huidobro, R. Manasevich and K. Schmitt, Mountain pass solutions for quasilinear elliptic equations, Calc. Var., 11 (2000), 33-67.
doi: 10.1007/s005260050002. |
[14] |
D. Costa and C. Magalhaes, Existence results for perturbations of the $p$-Laplacian, Nonlinear Anal., 24 (1995), 409-418.
doi: 10.1016/0362-546X(94)E0046-J. |
[15] |
M. Cuesta, D. deFigueiredo and J. P. Gossez, The beginning of the Fu$\brevec$ik spectrum for the $p$-Laplacian, J. Diff. Equas., 159 (1999), 212-238.
doi: 10.1006/jdeq.1999.3645. |
[16] |
M. Cuesta and P. Takac, A strong comparison principle for positive solutions of degenerate elliptic equations, Diff. Integ. Equas., 13 (2000), 721-746. |
[17] |
N. Dancer, On domain perturbation for super-linear Neumann problems and a question of Y. Lou, W-M Ni and L. Su, Discrete Cont Dyn Systems, 32 (2012), 3861-3869. |
[18] |
P. De Napoli and M. C. Mariani, Mountain pass solutions to equations of $p$-Laplacian type, Nonlinear Anal., (2003), 1205-1219.
doi: 10.1016/S0362-546X(03)00105-6. |
[19] |
M. Degiovanni and M. Scaglia, A variational approach to semilinear elliptic equations with measure data, Discrete and Continuous Dynamical Systems, 31 (2011), 1233-1248.
doi: 10.3934/dcds.2011.31.1233. |
[20] |
Y. Deng, S. Peng and L. Wang, Existence of multiple solutions for a nonhomogeneous semilinear elliptic equatio involving critical exponent, Discrete Contin. Dynam. Systems, 32 (2012), 795-826. |
[21] |
C. H. Derrick, Comments on nonlinear wave equations as model elementary particles, J. Math. Phys., 5 (1964), 1252-1254.
doi: 10.1063/1.1704233. |
[22] |
J. I. Diaz and J. E. Saa, Existence et unicité de solutions positives pour certaines equations elliptiques quasilineaires, CRAS, Paris t., 305 (1987), 521-524. |
[23] |
N. Dunford and J.Schwartz, "Linear Operators I,", Wiley-Interscience, ().
|
[24] |
G. Fei, On periodic solutions of superquadratic Hamiltonian systems, Elec. J. Diff. Equas., 8 (2002), 1-12. |
[25] |
D. deFigueiredo, Positive solutions of semilinear elliptic problems, in "Lecture Notes Math.," vol. 957, Springer, New York, (1982), 34-85. |
[26] |
M. Filippakis, A. Kristaly and N. S. Papageorgiou, Existence of five nonzero solutions with exact sign for a $p$-Laplacian equation, Discrete Cont Dyn Systems, 24 (2009), 405-440.
doi: 10.3934/dcds.2009.24.405. |
[27] |
J. Garcia Azorero, J. Manfredi and I. Peral Alonso, Sobolev versus Hölder local minimizers and globla multiplicity for some quasilinear elliptic equations, Comm. Contemp. Math., 2 (2000), 385-404.
doi: 10.1142/S0219199700000190. |
[28] |
L. Gasinski and N. S. Papageorgiou, "Nonlinear Analysis," Chapman & Hall/CRC, Boca Raton, 2006. |
[29] |
L. Gasinski and N. S. Papageorgiou, Existence and multiplicity of solutions for Neumann $p$-Laplacian type equations, Adv. Nonlin. Studies, 8 (2008), 843-870. |
[30] |
L. Gasinski and N. S. Papageorgiou, Multiple solutions for nonlinear coersive problems with a nonhomogeneous differential operator and a nonsmooth potential, Set Valued Var. Anal., 20 (2012), 417-443.
doi: 10.1007/s11228-011-0198-4. |
[31] |
D. Gilberg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer, Berlin, 1983.
doi: 10.1007/978-3-642-61798-0. |
[32] |
M. Guedda and L. Veron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlin. Anal., 13 (1989), 879-902.
doi: 10.1016/0362-546X(89)90020-5. |
[33] |
Z. Guo and Z. Liu, Perturbed elliptic equations with oscillatory nonlinearities, Discrete Cont Dyn Systems, 32 (2012), 3567-3585.
doi: 10.3934/dcds.2012.32.3567. |
[34] |
Z. Guo, Z. Liu, J. Wei and F. Zhou, Bifurcations of some elliptic problems with a singular nonlinearity via Morse index, Comm. Pure. Appl. Anal., 10 (2011), 507-525.
doi: 10.3934/cpaa.2011.10.507. |
[35] |
Shouchuan Hu and N. S. Papageorgiou, Positive solutions for nonlinear hemivariational inequalities, J. Math. Anal. Appl., 310 (2005), 161-176.
doi: 10.1016/j.jmaa.2005.01.051. |
[36] |
Shouchuan Hu and N. S. Papageorgiou, Nonlinear Neumann equations driven by a nonhomogeneous differential operator, Comm. Pure Appl. Anal., 9 (2010), 1801-1827. |
[37] |
Shouchuan Hu and N. S. Papageorgiou, Double resonance for Dirichlet problems with unbounded indefinite potential and combined nonlinearities, Comm. Pure Applied Anal., 11 (2012), 2005-2021.
doi: 10.3934/cpaa.2012.11.2005. |
[38] |
J. Garcia Melian, J. Rossi and J. Sabina de Lis, A convex-concave problem with a parameter on the boundary condition, Discrete Contin. Dynam. Systems, 32 (2012), 1095-1124. |
[39] |
L. Jeanjean, On the existence of bounded Palais-Smale sequences and applications to Landesmann-Lazer type problems in $\rn$, Proc. Royal Soc. Edinburgh, 129A (1999), 767-809. |
[40] |
A. Kristaly, M. Mihaileseu and V. Radulescu, Two nontrivial solutions for a nonhomogeneous Neumann problem: an Orlicz-Sobolev space setting, Proc. Royal. Soc. Edinburgh, 139A (2009), 367-379.
doi: 10.1017/S030821050700025X. |
[41] |
S. Kyritsi, D. O'Regan and N. S. Papageorgiou, Multiple solutions for resonant hemivariational inequalities via minimax methods, Adv. Nonlin. Studies, 9 (2009), 453-478. |
[42] |
S. Kyritsi and N. S. Papageorgiou, Multiple solutions for nonlinear elliptic equations with asymmetric reaction term, Discrete Cont Dyn Systems, 33 (2013), 2469-2494. |
[43] |
O. A. Ladyzhenskaya and N. Uraltseva, "Linear and Quasilinear Elliptic Equations," Academic Press, New York, 1968. |
[44] |
G. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Uraltseva for elliptic equations, Comm. Part. Diff. Equas., 16 (1991), 311-361.
doi: 10.1080/03605309108820761. |
[45] |
S. Li, S. Wu and H. Zhou, Solutions to semilinear elliptic problems with combined nonlinearities, J. Diff. Equas., 185 (2002), 200-224.
doi: 10.1006/jdeq.2001.4167. |
[46] |
M. Mihailescu, Existence and multiplicity of weak solutions for a class of degenerate nonlinear ellipitc equations, Boundary Value Problems, (2006), article ID 41295, 1-17. |
[47] |
M. Mihailescu and V. Radulescu, Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting, J. Math. Anal. Appl., 330 (2007), 416-432.
doi: 10.1016/j.jmaa.2006.07.082. |
[48] |
M. L. Miotto, Multiple solutions for elliptic problems in $R^N$ with critical Spbolev exponent and weight function, Comm. Pure Appl. Anal., 9 (2010), 233-248.
doi: 10.3934/cpaa.2010.9.233. |
[49] |
S. Miyajima, D. Motreanu and M. Tanaka, Multiple existence results of solutions for Neumann problems via super- and sub-solutions, J. Functional Anal., 262 (2012), 1921-1953.
doi: 10.1016/j.jfa.2011.11.028. |
[50] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, On $p$-Laplace equations with concave terms and asymmetric nonlinearities, Proc. Royal Soc. Edinburgh, 141A (2011), 171-192.
doi: 10.1017/S0308210509001656. |
[51] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Multiple constant sign and nodal solutions for nonlinear Neumann eigenvalue problems, Annali Scuola Normale Sup. Pisa, X (2011), 729-756. |
[52] |
D. Motreanu, D. O'Regan and N. S. Papageorgiou, A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems, Comm. Pure Appl. Anal., 10 (2011), 1791-1816.
doi: 10.3934/cpaa.2011.10.1791. |
[53] |
D. Motreanu and N. S. Papageorgiou, Existence and multiplicity of solutions for Neumann problems, J. Diff. Equas., 232 (2007), 1-35.
doi: 10.1016/j.jde.2006.09.008. |
[54] |
D. Motreanu and N. S. Papageorgiou, Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator, Proc. Amer. Math. Soc., 139 (2011), 3527-3535.
doi: 10.1090/S0002-9939-2011-10884-0. |
[55] |
N. S. Papageorgiou and S. Th. Kyritsi, "Handbook of Applied Analysis," Springer, New York, 2009. |
[56] |
N. S. Papageorgiou and E. M. Rocha, On nonlinear parametric problems for $p$-Laplacian like operators, RACSAM, 103 (2009), 177-200.
doi: 10.1007/BF03191850. |
[57] |
N. S. Papageorgiou, E. M. Rocha and V. Staicu, A multiplicity theorem for hemivariational inequalities with a $p$-Laplacian like differential operator, Nonlin. Anal., 69 (2008), 1150-1163.
doi: 10.1016/j.na.2007.06.023. |
[58] |
P. Pucci and J. Serrin, The strong maximum principle revisited, J. Diff. Equas., 196 (2004), 1-68; Erratum, J. Diff. Equas., 207 (2004), 226-227. |
[59] |
P. Pucci and J. Serrin, "The Maximum Principle," Birkhauser, Basel, 2007.
doi: 10.1016/j.jde.2004.09.002. |
[60] |
J. M. Rakotoson, Generalized eigenvalue problem for totally discontinuous operator, Discrete Contin. Dynam. Systems, 28 (2010), 343-373.
doi: 10.3934/dcds.2010.28.343. |
[61] |
P. Roselli and B. Sciunzi, A strong comparison principle for the $p$-Laplacian, Proc. Amer. Math. Soc., 135 (2007), 3217-3224.
doi: 10.1090/S0002-9939-07-08847-8. |
[62] |
M. Sun, Multiplicity of solutions for a class of quasilinear elliptic equation at resonance, J. Math. Anal. Appl., 386 (2012), 661-668.
doi: 10.1016/j.jmaa.2011.08.030. |
[63] |
J. Vazquez, A strong maximum principle for some quailinear elliptic equations, Appl. Math. Optim., 12 (1984), 191-202.
doi: 10.1007/BF01449041. |
[64] |
R. Zhang, J. Chen and F. Zhan, Multiple solutions for superlinear elliptic systems of Hamiltonian type, Discrete Cont Dyn Systems, 30 (2011), 1249-1262.
doi: 10.3934/dcds.2011.30.1249. |
show all references
References:
[1] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, The spectrum and an index formula for the Neumann $p$-Laplacian and multiple solutions for problems with a crossing nonlinearity, Discrete Cont Dyn Systems, 25 (2009), 431-456. |
[2] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, On a $p$-superlinear Neumann $p$-Laplacian equation, Topol. Methods Nonlin. Anal., 34 (2009), 111-130. |
[3] |
A. Allendes and A. Quaas, Multiplicity results for extremal operators through bifurcation, Discrete Cont Dyn Systems, 29 (2011), 51-65. |
[4] |
D. Arcoya and D. Ruiz, The Ambrosetti-Prodi problem for the $p$-Laplace operator, Comm. Part. Diff. Equs., 31 (2006), 849-863.
doi: 10.1080/03605300500394447. |
[5] |
V. Benci, P. D'Avenia, D. Fortunato and L. Pisani, Solitons in several space dimensions: Derrick's problem and infinitely many solutions, Arch. Rational Mech. Anal., 154 (2000), 297-324.
doi: 10.1007/s002050000101. |
[6] |
R. Benguria, H. Brezis and E. H. Lieb, The Thomas-Fermi-von Weizsäcker theory of atoms and molecules, Comm. Math. Physics, 79 (1981), 167-180.
doi: 10.1007/BF01942059. |
[7] |
H. Brezis and L. Nirenberg, $H^1$ versus $C^1$ local minimizers, CRAS Paris t., 317 (1993), 465-472. |
[8] |
S. Cano-Casanova, Coercivity of elliptic mixed boundary value problems in annulus of $\mathbbR^N$, Discrete and Continuous Dynamical Systems, 32 (2012), 3819-3839.
doi: 10.3934/dcds.2012.32.3819. |
[9] |
K. C. Chang, "Methods of Nonilnear Analysis," Springer, Berlin (2005). |
[10] |
S. Cingolani and M. Degiovanni, Nontrivial solutions for $p$-Laplacian equations with right hand side having $p$-linear growth, Comm. Part. Diff. Equas., 30 (2005), 1191-1203.
doi: 10.1080/03605300500257594. |
[11] |
S. Cingolani and G. Vannella, Critical groups computations on a class of Sobolev Banach spaces via Morse index, ann. Inst. H. Poincare-AN, 20 (2003), 271-292. |
[12] |
S. Cingolani and G. Vannella, Marino-Prodi perturbation type results and Morse indices of minimaz critical points for a class of functionals in Banach spaces, Annali di Mat. Pura Appl., 186 (2007), 155-183.
doi: 10.1007/s10231-005-0176-2. |
[13] |
P. Clement, M.Garcia Huidobro, R. Manasevich and K. Schmitt, Mountain pass solutions for quasilinear elliptic equations, Calc. Var., 11 (2000), 33-67.
doi: 10.1007/s005260050002. |
[14] |
D. Costa and C. Magalhaes, Existence results for perturbations of the $p$-Laplacian, Nonlinear Anal., 24 (1995), 409-418.
doi: 10.1016/0362-546X(94)E0046-J. |
[15] |
M. Cuesta, D. deFigueiredo and J. P. Gossez, The beginning of the Fu$\brevec$ik spectrum for the $p$-Laplacian, J. Diff. Equas., 159 (1999), 212-238.
doi: 10.1006/jdeq.1999.3645. |
[16] |
M. Cuesta and P. Takac, A strong comparison principle for positive solutions of degenerate elliptic equations, Diff. Integ. Equas., 13 (2000), 721-746. |
[17] |
N. Dancer, On domain perturbation for super-linear Neumann problems and a question of Y. Lou, W-M Ni and L. Su, Discrete Cont Dyn Systems, 32 (2012), 3861-3869. |
[18] |
P. De Napoli and M. C. Mariani, Mountain pass solutions to equations of $p$-Laplacian type, Nonlinear Anal., (2003), 1205-1219.
doi: 10.1016/S0362-546X(03)00105-6. |
[19] |
M. Degiovanni and M. Scaglia, A variational approach to semilinear elliptic equations with measure data, Discrete and Continuous Dynamical Systems, 31 (2011), 1233-1248.
doi: 10.3934/dcds.2011.31.1233. |
[20] |
Y. Deng, S. Peng and L. Wang, Existence of multiple solutions for a nonhomogeneous semilinear elliptic equatio involving critical exponent, Discrete Contin. Dynam. Systems, 32 (2012), 795-826. |
[21] |
C. H. Derrick, Comments on nonlinear wave equations as model elementary particles, J. Math. Phys., 5 (1964), 1252-1254.
doi: 10.1063/1.1704233. |
[22] |
J. I. Diaz and J. E. Saa, Existence et unicité de solutions positives pour certaines equations elliptiques quasilineaires, CRAS, Paris t., 305 (1987), 521-524. |
[23] |
N. Dunford and J.Schwartz, "Linear Operators I,", Wiley-Interscience, ().
|
[24] |
G. Fei, On periodic solutions of superquadratic Hamiltonian systems, Elec. J. Diff. Equas., 8 (2002), 1-12. |
[25] |
D. deFigueiredo, Positive solutions of semilinear elliptic problems, in "Lecture Notes Math.," vol. 957, Springer, New York, (1982), 34-85. |
[26] |
M. Filippakis, A. Kristaly and N. S. Papageorgiou, Existence of five nonzero solutions with exact sign for a $p$-Laplacian equation, Discrete Cont Dyn Systems, 24 (2009), 405-440.
doi: 10.3934/dcds.2009.24.405. |
[27] |
J. Garcia Azorero, J. Manfredi and I. Peral Alonso, Sobolev versus Hölder local minimizers and globla multiplicity for some quasilinear elliptic equations, Comm. Contemp. Math., 2 (2000), 385-404.
doi: 10.1142/S0219199700000190. |
[28] |
L. Gasinski and N. S. Papageorgiou, "Nonlinear Analysis," Chapman & Hall/CRC, Boca Raton, 2006. |
[29] |
L. Gasinski and N. S. Papageorgiou, Existence and multiplicity of solutions for Neumann $p$-Laplacian type equations, Adv. Nonlin. Studies, 8 (2008), 843-870. |
[30] |
L. Gasinski and N. S. Papageorgiou, Multiple solutions for nonlinear coersive problems with a nonhomogeneous differential operator and a nonsmooth potential, Set Valued Var. Anal., 20 (2012), 417-443.
doi: 10.1007/s11228-011-0198-4. |
[31] |
D. Gilberg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer, Berlin, 1983.
doi: 10.1007/978-3-642-61798-0. |
[32] |
M. Guedda and L. Veron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlin. Anal., 13 (1989), 879-902.
doi: 10.1016/0362-546X(89)90020-5. |
[33] |
Z. Guo and Z. Liu, Perturbed elliptic equations with oscillatory nonlinearities, Discrete Cont Dyn Systems, 32 (2012), 3567-3585.
doi: 10.3934/dcds.2012.32.3567. |
[34] |
Z. Guo, Z. Liu, J. Wei and F. Zhou, Bifurcations of some elliptic problems with a singular nonlinearity via Morse index, Comm. Pure. Appl. Anal., 10 (2011), 507-525.
doi: 10.3934/cpaa.2011.10.507. |
[35] |
Shouchuan Hu and N. S. Papageorgiou, Positive solutions for nonlinear hemivariational inequalities, J. Math. Anal. Appl., 310 (2005), 161-176.
doi: 10.1016/j.jmaa.2005.01.051. |
[36] |
Shouchuan Hu and N. S. Papageorgiou, Nonlinear Neumann equations driven by a nonhomogeneous differential operator, Comm. Pure Appl. Anal., 9 (2010), 1801-1827. |
[37] |
Shouchuan Hu and N. S. Papageorgiou, Double resonance for Dirichlet problems with unbounded indefinite potential and combined nonlinearities, Comm. Pure Applied Anal., 11 (2012), 2005-2021.
doi: 10.3934/cpaa.2012.11.2005. |
[38] |
J. Garcia Melian, J. Rossi and J. Sabina de Lis, A convex-concave problem with a parameter on the boundary condition, Discrete Contin. Dynam. Systems, 32 (2012), 1095-1124. |
[39] |
L. Jeanjean, On the existence of bounded Palais-Smale sequences and applications to Landesmann-Lazer type problems in $\rn$, Proc. Royal Soc. Edinburgh, 129A (1999), 767-809. |
[40] |
A. Kristaly, M. Mihaileseu and V. Radulescu, Two nontrivial solutions for a nonhomogeneous Neumann problem: an Orlicz-Sobolev space setting, Proc. Royal. Soc. Edinburgh, 139A (2009), 367-379.
doi: 10.1017/S030821050700025X. |
[41] |
S. Kyritsi, D. O'Regan and N. S. Papageorgiou, Multiple solutions for resonant hemivariational inequalities via minimax methods, Adv. Nonlin. Studies, 9 (2009), 453-478. |
[42] |
S. Kyritsi and N. S. Papageorgiou, Multiple solutions for nonlinear elliptic equations with asymmetric reaction term, Discrete Cont Dyn Systems, 33 (2013), 2469-2494. |
[43] |
O. A. Ladyzhenskaya and N. Uraltseva, "Linear and Quasilinear Elliptic Equations," Academic Press, New York, 1968. |
[44] |
G. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Uraltseva for elliptic equations, Comm. Part. Diff. Equas., 16 (1991), 311-361.
doi: 10.1080/03605309108820761. |
[45] |
S. Li, S. Wu and H. Zhou, Solutions to semilinear elliptic problems with combined nonlinearities, J. Diff. Equas., 185 (2002), 200-224.
doi: 10.1006/jdeq.2001.4167. |
[46] |
M. Mihailescu, Existence and multiplicity of weak solutions for a class of degenerate nonlinear ellipitc equations, Boundary Value Problems, (2006), article ID 41295, 1-17. |
[47] |
M. Mihailescu and V. Radulescu, Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting, J. Math. Anal. Appl., 330 (2007), 416-432.
doi: 10.1016/j.jmaa.2006.07.082. |
[48] |
M. L. Miotto, Multiple solutions for elliptic problems in $R^N$ with critical Spbolev exponent and weight function, Comm. Pure Appl. Anal., 9 (2010), 233-248.
doi: 10.3934/cpaa.2010.9.233. |
[49] |
S. Miyajima, D. Motreanu and M. Tanaka, Multiple existence results of solutions for Neumann problems via super- and sub-solutions, J. Functional Anal., 262 (2012), 1921-1953.
doi: 10.1016/j.jfa.2011.11.028. |
[50] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, On $p$-Laplace equations with concave terms and asymmetric nonlinearities, Proc. Royal Soc. Edinburgh, 141A (2011), 171-192.
doi: 10.1017/S0308210509001656. |
[51] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Multiple constant sign and nodal solutions for nonlinear Neumann eigenvalue problems, Annali Scuola Normale Sup. Pisa, X (2011), 729-756. |
[52] |
D. Motreanu, D. O'Regan and N. S. Papageorgiou, A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems, Comm. Pure Appl. Anal., 10 (2011), 1791-1816.
doi: 10.3934/cpaa.2011.10.1791. |
[53] |
D. Motreanu and N. S. Papageorgiou, Existence and multiplicity of solutions for Neumann problems, J. Diff. Equas., 232 (2007), 1-35.
doi: 10.1016/j.jde.2006.09.008. |
[54] |
D. Motreanu and N. S. Papageorgiou, Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator, Proc. Amer. Math. Soc., 139 (2011), 3527-3535.
doi: 10.1090/S0002-9939-2011-10884-0. |
[55] |
N. S. Papageorgiou and S. Th. Kyritsi, "Handbook of Applied Analysis," Springer, New York, 2009. |
[56] |
N. S. Papageorgiou and E. M. Rocha, On nonlinear parametric problems for $p$-Laplacian like operators, RACSAM, 103 (2009), 177-200.
doi: 10.1007/BF03191850. |
[57] |
N. S. Papageorgiou, E. M. Rocha and V. Staicu, A multiplicity theorem for hemivariational inequalities with a $p$-Laplacian like differential operator, Nonlin. Anal., 69 (2008), 1150-1163.
doi: 10.1016/j.na.2007.06.023. |
[58] |
P. Pucci and J. Serrin, The strong maximum principle revisited, J. Diff. Equas., 196 (2004), 1-68; Erratum, J. Diff. Equas., 207 (2004), 226-227. |
[59] |
P. Pucci and J. Serrin, "The Maximum Principle," Birkhauser, Basel, 2007.
doi: 10.1016/j.jde.2004.09.002. |
[60] |
J. M. Rakotoson, Generalized eigenvalue problem for totally discontinuous operator, Discrete Contin. Dynam. Systems, 28 (2010), 343-373.
doi: 10.3934/dcds.2010.28.343. |
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P. Roselli and B. Sciunzi, A strong comparison principle for the $p$-Laplacian, Proc. Amer. Math. Soc., 135 (2007), 3217-3224.
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