October  2011, 7(4): 991-1002. doi: 10.3934/jimo.2011.7.991

Multiple solutions for a class of semilinear elliptic variational inclusion problems

1. 

Department of Mathematics, Soochow University, Suzhou, 215006, China, China

Received  September 2010 Revised  July 2011 Published  August 2011

In this paper, by using a local linking theorem, we obtain the existence of multiple solutions for a class of semilinear elliptic variational inclusion problems at non-resonance.
Citation: Rong Xiao, Yuying Zhou. Multiple solutions for a class of semilinear elliptic variational inclusion problems. Journal of Industrial and Management Optimization, 2011, 7 (4) : 991-1002. doi: 10.3934/jimo.2011.7.991
References:
[1]

F. H. Clarke, "Optimization and Nonsmooth Analysis," Canadian Mathematical Society Series of Monographs and Advanced Texts, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1983.

[2]

Z. Denkowski, L. Gasinski and N. S. Papageorgiou, Existence and multiplicity of solutions for semilinear hemivariational inequalities at resonance, Nonlinear Anal., 66 (2007), 1329-1340. doi: 10.1016/j.na.2006.01.019.

[3]

L. Gasinski and N. S. Papageorgiou, "Nonlinear Analysis," Series in Mathematical Analysis and Applications, 9, Chapman & Hall/CRC, Boca Raton, FL, 2006.

[4]

M. Filippakis, L. Gasinski and N. S. Papageorgiou, A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential, Nonlinear Anal., 61 (2005), 61-75. doi: 10.1016/j.na.2004.11.012.

[5]

Z. Denkowski, L. Gasinski and N. S. Papageorgiou, Nontrivial solutions for resonant hemivariational inequalities, J. Global Optim., 34 (2006), 317-337. doi: 10.1007/s10898-005-4388-1.

[6]

L. Gasinski 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, FL, 2005.

[7]

X. X. Huang and X. Q. Yang, Levitin-Polyak well-posedness in generalized variational inequality problems with functional constraints, J. Ind. Manag. Optim., 3 (2007), 671-684.

[8]

G. Idone and A. Maugeri, Variational inequalities and a transport planning for an elastic and continuum model, J. Ind. Manag. Optim., 1 (2005), 81-86.

[9]

N. S. Papageorgiou, S. R. Andrade Santos and V. Staicu, Eigenvalue problems for hemivariational inequalities, Set-Valued Anal., 16 (2008), 1061-1087. doi: 10.1007/s11228-008-0100-1.

[10]

C.-L. Tang and Q.-J. Gao, Elliptic resonant problems at higher eigenvalues with an unbounded nonlinear term, J. Diff. Equat., 146 (1998), 56-66. doi: 10.1006/jdeq.1998.3411.

[11]

C.-L. Tang, Multiple solutions of Neumann problem for elliptic equations, Nonlinear Anal., 54 (2003), 637-650. doi: 10.1016/S0362-546X(03)00091-9.

[12]

L. Wang, Y. Li and L. W. Zhang, A differential equation method for solving box constrained variational inequality problems, J. Ind. Manag. Optim., 7 (2011), 183-198.

show all references

References:
[1]

F. H. Clarke, "Optimization and Nonsmooth Analysis," Canadian Mathematical Society Series of Monographs and Advanced Texts, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1983.

[2]

Z. Denkowski, L. Gasinski and N. S. Papageorgiou, Existence and multiplicity of solutions for semilinear hemivariational inequalities at resonance, Nonlinear Anal., 66 (2007), 1329-1340. doi: 10.1016/j.na.2006.01.019.

[3]

L. Gasinski and N. S. Papageorgiou, "Nonlinear Analysis," Series in Mathematical Analysis and Applications, 9, Chapman & Hall/CRC, Boca Raton, FL, 2006.

[4]

M. Filippakis, L. Gasinski and N. S. Papageorgiou, A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential, Nonlinear Anal., 61 (2005), 61-75. doi: 10.1016/j.na.2004.11.012.

[5]

Z. Denkowski, L. Gasinski and N. S. Papageorgiou, Nontrivial solutions for resonant hemivariational inequalities, J. Global Optim., 34 (2006), 317-337. doi: 10.1007/s10898-005-4388-1.

[6]

L. Gasinski 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, FL, 2005.

[7]

X. X. Huang and X. Q. Yang, Levitin-Polyak well-posedness in generalized variational inequality problems with functional constraints, J. Ind. Manag. Optim., 3 (2007), 671-684.

[8]

G. Idone and A. Maugeri, Variational inequalities and a transport planning for an elastic and continuum model, J. Ind. Manag. Optim., 1 (2005), 81-86.

[9]

N. S. Papageorgiou, S. R. Andrade Santos and V. Staicu, Eigenvalue problems for hemivariational inequalities, Set-Valued Anal., 16 (2008), 1061-1087. doi: 10.1007/s11228-008-0100-1.

[10]

C.-L. Tang and Q.-J. Gao, Elliptic resonant problems at higher eigenvalues with an unbounded nonlinear term, J. Diff. Equat., 146 (1998), 56-66. doi: 10.1006/jdeq.1998.3411.

[11]

C.-L. Tang, Multiple solutions of Neumann problem for elliptic equations, Nonlinear Anal., 54 (2003), 637-650. doi: 10.1016/S0362-546X(03)00091-9.

[12]

L. Wang, Y. Li and L. W. Zhang, A differential equation method for solving box constrained variational inequality problems, J. Ind. Manag. Optim., 7 (2011), 183-198.

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