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 & 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, (1983).   Google Scholar

[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.  doi: 10.1016/j.na.2006.01.019.  Google Scholar

[3]

L. Gasinski and N. S. Papageorgiou, "Nonlinear Analysis,", Series in Mathematical Analysis and Applications, 9 (2006).   Google Scholar

[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.  doi: 10.1016/j.na.2004.11.012.  Google Scholar

[5]

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

[6]

L. Gasinski and N. S. Papageorgiou, "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems,", Series in Mathematical Analysis and Applications, 8 (2005).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[9]

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

[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.  doi: 10.1006/jdeq.1998.3411.  Google Scholar

[11]

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

[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.   Google Scholar

show all references

References:
[1]

F. H. Clarke, "Optimization and Nonsmooth Analysis,", Canadian Mathematical Society Series of Monographs and Advanced Texts, (1983).   Google Scholar

[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.  doi: 10.1016/j.na.2006.01.019.  Google Scholar

[3]

L. Gasinski and N. S. Papageorgiou, "Nonlinear Analysis,", Series in Mathematical Analysis and Applications, 9 (2006).   Google Scholar

[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.  doi: 10.1016/j.na.2004.11.012.  Google Scholar

[5]

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

[6]

L. Gasinski and N. S. Papageorgiou, "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems,", Series in Mathematical Analysis and Applications, 8 (2005).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[9]

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

[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.  doi: 10.1006/jdeq.1998.3411.  Google Scholar

[11]

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

[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.   Google Scholar

[1]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825

[2]

Jon Aaronson, Dalia Terhesiu. Local limit theorems for suspended semiflows. Discrete & Continuous Dynamical Systems - A, 2020, 40 (12) : 6575-6609. doi: 10.3934/dcds.2020294

[3]

Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233

[4]

Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco. Linear nonbinary covering codes and saturating sets in projective spaces. Advances in Mathematics of Communications, 2011, 5 (1) : 119-147. doi: 10.3934/amc.2011.5.119

[5]

Charles Fulton, David Pearson, Steven Pruess. Characterization of the spectral density function for a one-sided tridiagonal Jacobi matrix operator. Conference Publications, 2013, 2013 (special) : 247-257. doi: 10.3934/proc.2013.2013.247

[6]

Seung-Yeal Ha, Shi Jin. Local sensitivity analysis for the Cucker-Smale model with random inputs. Kinetic & Related Models, 2018, 11 (4) : 859-889. doi: 10.3934/krm.2018034

[7]

Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (5) : 1649-1672. doi: 10.3934/dcdss.2020448

[8]

Rabiaa Ouahabi, Nasr-Eddine Hamri. Design of new scheme adaptive generalized hybrid projective synchronization for two different chaotic systems with uncertain parameters. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2361-2370. doi: 10.3934/dcdsb.2020182

[9]

Carlos Gutierrez, Nguyen Van Chau. A remark on an eigenvalue condition for the global injectivity of differentiable maps of $R^2$. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 397-402. doi: 10.3934/dcds.2007.17.397

[10]

Mansour Shrahili, Ravi Shanker Dubey, Ahmed Shafay. Inclusion of fading memory to Banister model of changes in physical condition. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 881-888. doi: 10.3934/dcdss.2020051

[11]

Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (26)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]