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Multiple solutions for a Neumann-type differential inclusion problem involving the $p(\cdot)$-Laplacian
Multiple solutions to a Neumann problem with equi-diffusive reaction term
1. | Engineering Faculty, University of Messina, 98166 Messina, Italy |
2. | Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania |
3. | Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780 |
References:
[1] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, Existence of multiple solutions with precise sign information for superlinear Neumann problems, Ann. Mat. Pura Appl. (4), 188 (2009), 679-719.
doi: 10.1007/s10231-009-0096-7. |
[2] |
P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with "strong'' resonance at infinity, Nonlinear Anal., 7 (1983), 981-1012.
doi: 10.1016/0362-546X(83)90115-3. |
[3] |
T. Bartsch, K.-C. Chang and Z.-Q. Wang, On the Morse indices of sign changing solutions of nonlinear elliptic problems, Math. Z., 233 (2000), 655-677.
doi: 10.1007/s002090050492. |
[4] |
T. Bartsch and S. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance, Nonlinear Anal., 28 (1997), 419-441.
doi: 10.1016/0362-546X(95)00167-T. |
[5] |
K.-C. Chang, "Methods in Nonlinear Analysis," Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005. |
[6] |
A. Kristály and N. S. Papageorgiou, Multiple nontrivial solutions for Neumann problems involving the $p$-Laplacian: A Morse theoretical approach, Adv. Nonlinear Stud., 10 (2010), 83-107. |
[7] |
S. T. Kyritsi and N. S. Papageorgiou, Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue, Matematiche (Catania), 65 (2010), 79-95. |
[8] |
An Lê, Eigenvalue problems for the $p$-Laplacian, Nonlinear Anal., 64 (2006), 1057-1099.
doi: 10.1016/j.na.2005.06.024. |
[9] |
S. A. Marano and N. S. Papageorgiou, On a Neumann problem with $p$-Laplacian and non-coercive resonant nonlinearity, Pacific J. Math., in press. |
[10] |
S. A. Marano and N. S. Papageorgiou, Constant-sign and nodal solutions for a Neumann problem with $p$-Laplacian and equi-diffusive reaction term, Topol. Methods Nonlinear Anal., 38 (2011), in press. |
[11] |
J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems," Appl. Math. Sci., 74, Springer-Verlag, New York, 1989. |
[12] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations, Manuscripta Math., 124 (2007), 507-531.
doi: 10.1007/s00229-007-0127-x. |
[13] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Nonlinear Neumann problems near resonance, Indiana Univ. Math. J., 58 (2009), 1257-1279.
doi: 10.1512/iumj.2009.58.3565. |
[14] |
W. Zou and J. Q. Liu, Multiple solutions for resonant elliptic equations via local linking theory and Morse theory, J. Differential Equations, 170 (2001), 68-95.
doi: 10.1006/jdeq.2000.3812. |
show all references
References:
[1] |
S. Aizicovici, N. S. Papageorgiou and V. Staicu, Existence of multiple solutions with precise sign information for superlinear Neumann problems, Ann. Mat. Pura Appl. (4), 188 (2009), 679-719.
doi: 10.1007/s10231-009-0096-7. |
[2] |
P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with "strong'' resonance at infinity, Nonlinear Anal., 7 (1983), 981-1012.
doi: 10.1016/0362-546X(83)90115-3. |
[3] |
T. Bartsch, K.-C. Chang and Z.-Q. Wang, On the Morse indices of sign changing solutions of nonlinear elliptic problems, Math. Z., 233 (2000), 655-677.
doi: 10.1007/s002090050492. |
[4] |
T. Bartsch and S. Li, Critical point theory for asymptotically quadratic functionals and applications to problems with resonance, Nonlinear Anal., 28 (1997), 419-441.
doi: 10.1016/0362-546X(95)00167-T. |
[5] |
K.-C. Chang, "Methods in Nonlinear Analysis," Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005. |
[6] |
A. Kristály and N. S. Papageorgiou, Multiple nontrivial solutions for Neumann problems involving the $p$-Laplacian: A Morse theoretical approach, Adv. Nonlinear Stud., 10 (2010), 83-107. |
[7] |
S. T. Kyritsi and N. S. Papageorgiou, Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue, Matematiche (Catania), 65 (2010), 79-95. |
[8] |
An Lê, Eigenvalue problems for the $p$-Laplacian, Nonlinear Anal., 64 (2006), 1057-1099.
doi: 10.1016/j.na.2005.06.024. |
[9] |
S. A. Marano and N. S. Papageorgiou, On a Neumann problem with $p$-Laplacian and non-coercive resonant nonlinearity, Pacific J. Math., in press. |
[10] |
S. A. Marano and N. S. Papageorgiou, Constant-sign and nodal solutions for a Neumann problem with $p$-Laplacian and equi-diffusive reaction term, Topol. Methods Nonlinear Anal., 38 (2011), in press. |
[11] |
J. Mawhin and M. Willem, "Critical Point Theory and Hamiltonian Systems," Appl. Math. Sci., 74, Springer-Verlag, New York, 1989. |
[12] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations, Manuscripta Math., 124 (2007), 507-531.
doi: 10.1007/s00229-007-0127-x. |
[13] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, Nonlinear Neumann problems near resonance, Indiana Univ. Math. J., 58 (2009), 1257-1279.
doi: 10.1512/iumj.2009.58.3565. |
[14] |
W. Zou and J. Q. Liu, Multiple solutions for resonant elliptic equations via local linking theory and Morse theory, J. Differential Equations, 170 (2001), 68-95.
doi: 10.1006/jdeq.2000.3812. |
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