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A variational approach to a class of quasilinear elliptic equations not in divergence form
Three solutions with precise sign properties for systems of quasilinear elliptic equations
1. | Université de Perpignan, Département de Mathématiques, 66860 Perpignan |
References:
[1] |
A. Anane, Simplicité et isolation de la première valeur propre du $p$-Laplacien avec poids, (French) [Simplicity and isolation of the first eigenvalue of the $p$-Laplacian with weight], C. R. Acad. Sci. Paris Sér. I Math., 305 (1987), 725-728. |
[2] |
D. Averna, S. A. Marano and D. Motreanu, Multiple solutions for a Dirichlet problem with $p$-Laplacian and set-valued nonlinearity, Bull. Aust. Math. Soc., 77 (2008), 285-303.
doi: 10.1017/S0004972708000282. |
[3] |
S. Carl, V. K. Le and D. Motreanu, "Nonsmooth Variational Problems and Their Inequalities. Comparison Principles and Applications," Springer Monographs in Mathematics, Springer, New York, 2007. |
[4] |
S. Carl and D. Motreanu, Constant-sign and sign-changing solutions for nonlinear eigenvalue problems, Nonlinear Anal., 68 (2008), 2668-2676.
doi: 10.1016/j.na.2007.02.013. |
[5] |
S. Carl and Z. Naniewicz, Vector quasi-hemivariational inequalities and discontinuous elliptic systems, J. Global Optim., 34 (2006), 609-634.
doi: 10.1007/s10898-005-1651-4. |
[6] |
S. Carl and K. Perera, Sign-changing and multiple solutions for the $p$-Laplacian, Abstr. Appl. Anal., 7 (2002), 613-625.
doi: 10.1155/S1085337502207010. |
[7] |
M. Cuesta, D. de Figueiredo and J.-P. Gossez, The beginning of the Fučik spectrum for the $p$-Laplacian, J. Differential Equations, 159 (1999), 212-238.
doi: 10.1006/jdeq.1999.3645. |
[8] |
L. Gasiński and N. S. Papageorgiou, "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems," Series in Mathematical Analysis and Applications, 8, Chapman & Hall/CRC, Boca Raton, 2005. |
[9] |
L. Gasiński and N. S. Papageorgiou, "Nonlinear Analysis," Series in Mathematical Analysis and Applications, 9, Chapman & Hall/CRC, Boca Raton, FL, 2006. |
[10] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, A unified approach for constant sign and nodal solutions, Adv. Differential Equations, 12 (2007), 1363-1392. |
[11] |
D. Motreanu and K. Perera, Multiple nontrivial solutions of Neumann $p$-Laplacian systems, Topol. Methods Nonlinear Anal., 34 (2009), 41-48. |
[12] |
D. Motreanu and Z. Zhang, Constant sign and sign changing solutions for systems of quasilinear elliptic equations, Set-Valued Var. Anal., 19 (2011), 255-269. |
[13] |
J. L. Vázquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optimization., 12 (1984), 191-202.
doi: 10.1007/BF01449041. |
[14] |
J. Zhang and Z. Zhang, Existence results for some nonlinear elliptic systems, Nonlinear Anal., 71 (2009), 2840-2846.
doi: 10.1016/j.na.2009.01.158. |
show all references
References:
[1] |
A. Anane, Simplicité et isolation de la première valeur propre du $p$-Laplacien avec poids, (French) [Simplicity and isolation of the first eigenvalue of the $p$-Laplacian with weight], C. R. Acad. Sci. Paris Sér. I Math., 305 (1987), 725-728. |
[2] |
D. Averna, S. A. Marano and D. Motreanu, Multiple solutions for a Dirichlet problem with $p$-Laplacian and set-valued nonlinearity, Bull. Aust. Math. Soc., 77 (2008), 285-303.
doi: 10.1017/S0004972708000282. |
[3] |
S. Carl, V. K. Le and D. Motreanu, "Nonsmooth Variational Problems and Their Inequalities. Comparison Principles and Applications," Springer Monographs in Mathematics, Springer, New York, 2007. |
[4] |
S. Carl and D. Motreanu, Constant-sign and sign-changing solutions for nonlinear eigenvalue problems, Nonlinear Anal., 68 (2008), 2668-2676.
doi: 10.1016/j.na.2007.02.013. |
[5] |
S. Carl and Z. Naniewicz, Vector quasi-hemivariational inequalities and discontinuous elliptic systems, J. Global Optim., 34 (2006), 609-634.
doi: 10.1007/s10898-005-1651-4. |
[6] |
S. Carl and K. Perera, Sign-changing and multiple solutions for the $p$-Laplacian, Abstr. Appl. Anal., 7 (2002), 613-625.
doi: 10.1155/S1085337502207010. |
[7] |
M. Cuesta, D. de Figueiredo and J.-P. Gossez, The beginning of the Fučik spectrum for the $p$-Laplacian, J. Differential Equations, 159 (1999), 212-238.
doi: 10.1006/jdeq.1999.3645. |
[8] |
L. Gasiński and N. S. Papageorgiou, "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems," Series in Mathematical Analysis and Applications, 8, Chapman & Hall/CRC, Boca Raton, 2005. |
[9] |
L. Gasiński and N. S. Papageorgiou, "Nonlinear Analysis," Series in Mathematical Analysis and Applications, 9, Chapman & Hall/CRC, Boca Raton, FL, 2006. |
[10] |
D. Motreanu, V. V. Motreanu and N. S. Papageorgiou, A unified approach for constant sign and nodal solutions, Adv. Differential Equations, 12 (2007), 1363-1392. |
[11] |
D. Motreanu and K. Perera, Multiple nontrivial solutions of Neumann $p$-Laplacian systems, Topol. Methods Nonlinear Anal., 34 (2009), 41-48. |
[12] |
D. Motreanu and Z. Zhang, Constant sign and sign changing solutions for systems of quasilinear elliptic equations, Set-Valued Var. Anal., 19 (2011), 255-269. |
[13] |
J. L. Vázquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optimization., 12 (1984), 191-202.
doi: 10.1007/BF01449041. |
[14] |
J. Zhang and Z. Zhang, Existence results for some nonlinear elliptic systems, Nonlinear Anal., 71 (2009), 2840-2846.
doi: 10.1016/j.na.2009.01.158. |
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