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Fourth-order hemivariational inequalities
Multiple solutions for a Navier boundary value problem involving the $p$--biharmonic operator
1. | DIMET - Facoltà di Ingegneria, Università di Reggio Calabria, Località Feo di Vito, 89100 Reggio Calabria, Italy |
2. | Dipartimento P.A.U., Università degli Studi Mediterranea di Reggio Calabria, Salita Melissari - Feo di Vito, 89100 Reggio Calabria, Italy |
References:
[1] |
G. Bonanno and B. Di Bella, A boundary value problem for fourth-order elastic beam equations, J. Math. Anal. Appl., 343 (2008), 1166-1176.
doi: 10.1016/j.jmaa.2008.01.049. |
[2] |
G. Bonanno and B. Di Bella, A fourth-order boundary value problem for a Sturm-Liouville type equation, Appl. Math. Comput., 217 (2010), 3635-3640.
doi: 10.1016/j.amc.2010.10.019. |
[3] |
G. Bonanno and B. Di Bella, Infinitely many solutions for a fourth-order elastic beam equation, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 357-368.
doi: 10.1007/s00030-011-0099-0. |
[4] |
G. Bonanno and P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations, 244 (2008), 3031-3059.
doi: 10.1016/j.jde.2008.02.025. |
[5] |
G. Bonanno and S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal., 89 (2010), 1-10.
doi: 10.1080/00036810903397438. |
[6] |
H. M. Guo and D. Geng, Infinitely many solutions for the Dirichlet problem involving the $p$-biharmonic-like equation, J. South China Normal Univ. Natur. Sci. Ed., 2009, 18-21, 28. |
[7] |
M. R. Grossinho, L. Sanchez and S. A. Tersian, On the solvability of a boundary value problem for a fourth-order ordinary differential equation, Appl. Math. Lett., 18 (2005), 439-444. |
[8] |
G. Han and Z. Xu, Multiple solutions of some nonlinear fourth-order beam equations, Nonlinear Anal., 68 (2008), 3646-3656.
doi: 10.1016/j.na.2007.04.007. |
[9] |
C. Li and C.-L. Tang, Three solutions for a Navier boundary value problem involving the $p$-biharmonic, Nonlinear Anal., 72 (2010), 1339-1347.
doi: 10.1016/j.na.2009.08.011. |
[10] |
X.-L. Liu and W.-T. Li, Existence and multiplicity of solutions for fourth-order boundary value problems with parameters, J. Math. Anal. Appl., 327 (2007), 362-375.
doi: 10.1016/j.jmaa.2006.04.021. |
[11] |
A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal., 31 (1998), 895-908.
doi: 10.1016/S0362-546X(97)00446-X. |
[12] |
B. Ricceri, A general variational principle and some of its applications. Fixed point theory with applications in nonlinear analysis, J. Comput. Appl. Math., 133 (2000), 401-410.
doi: 10.1016/S0377-0427(99)00269-1. |
[13] |
G. Talenti, Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 3 (1976), 697-718. |
[14] |
Y. Wang and Y. Shen, Infinitely many sign-changing solutions for a class of biharmonic equation without symmetry, Nonlinear Anal., 71 (2009), 967-977.
doi: 10.1016/j.na.2008.11.052. |
[15] |
W. Wang and P. Zhao, Nonuniformly nonlinear elliptic equations of $p$-biharmonic type, J. Math. Anal. Appl., 348 (2008), 730-738.
doi: 10.1016/j.jmaa.2008.07.068. |
[16] |
Z. Yang, D. Geng and H. Yan, Existence of nontrivial solutions in $p$-biharmonic problems with critical growth, (Chinese) Chinese Ann. Math. Ser. A, 27 (2006), 129-142. |
show all references
References:
[1] |
G. Bonanno and B. Di Bella, A boundary value problem for fourth-order elastic beam equations, J. Math. Anal. Appl., 343 (2008), 1166-1176.
doi: 10.1016/j.jmaa.2008.01.049. |
[2] |
G. Bonanno and B. Di Bella, A fourth-order boundary value problem for a Sturm-Liouville type equation, Appl. Math. Comput., 217 (2010), 3635-3640.
doi: 10.1016/j.amc.2010.10.019. |
[3] |
G. Bonanno and B. Di Bella, Infinitely many solutions for a fourth-order elastic beam equation, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 357-368.
doi: 10.1007/s00030-011-0099-0. |
[4] |
G. Bonanno and P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations, 244 (2008), 3031-3059.
doi: 10.1016/j.jde.2008.02.025. |
[5] |
G. Bonanno and S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal., 89 (2010), 1-10.
doi: 10.1080/00036810903397438. |
[6] |
H. M. Guo and D. Geng, Infinitely many solutions for the Dirichlet problem involving the $p$-biharmonic-like equation, J. South China Normal Univ. Natur. Sci. Ed., 2009, 18-21, 28. |
[7] |
M. R. Grossinho, L. Sanchez and S. A. Tersian, On the solvability of a boundary value problem for a fourth-order ordinary differential equation, Appl. Math. Lett., 18 (2005), 439-444. |
[8] |
G. Han and Z. Xu, Multiple solutions of some nonlinear fourth-order beam equations, Nonlinear Anal., 68 (2008), 3646-3656.
doi: 10.1016/j.na.2007.04.007. |
[9] |
C. Li and C.-L. Tang, Three solutions for a Navier boundary value problem involving the $p$-biharmonic, Nonlinear Anal., 72 (2010), 1339-1347.
doi: 10.1016/j.na.2009.08.011. |
[10] |
X.-L. Liu and W.-T. Li, Existence and multiplicity of solutions for fourth-order boundary value problems with parameters, J. Math. Anal. Appl., 327 (2007), 362-375.
doi: 10.1016/j.jmaa.2006.04.021. |
[11] |
A. M. Micheletti and A. Pistoia, Multiplicity results for a fourth-order semilinear elliptic problem, Nonlinear Anal., 31 (1998), 895-908.
doi: 10.1016/S0362-546X(97)00446-X. |
[12] |
B. Ricceri, A general variational principle and some of its applications. Fixed point theory with applications in nonlinear analysis, J. Comput. Appl. Math., 133 (2000), 401-410.
doi: 10.1016/S0377-0427(99)00269-1. |
[13] |
G. Talenti, Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 3 (1976), 697-718. |
[14] |
Y. Wang and Y. Shen, Infinitely many sign-changing solutions for a class of biharmonic equation without symmetry, Nonlinear Anal., 71 (2009), 967-977.
doi: 10.1016/j.na.2008.11.052. |
[15] |
W. Wang and P. Zhao, Nonuniformly nonlinear elliptic equations of $p$-biharmonic type, J. Math. Anal. Appl., 348 (2008), 730-738.
doi: 10.1016/j.jmaa.2008.07.068. |
[16] |
Z. Yang, D. Geng and H. Yan, Existence of nontrivial solutions in $p$-biharmonic problems with critical growth, (Chinese) Chinese Ann. Math. Ser. A, 27 (2006), 129-142. |
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