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Strongly nonlinear multivalued elliptic equations on a bounded domain

Author

Listed:
  • Claudianor Alves
  • José Gonçalves
  • Jefferson Santos

Abstract

In this work we study the existence of nontrivial solution for the following class of multivalued quasilinear problems $$\begin{aligned} \displaystyle -\text{ div } ( \phi (|\nabla u|) \nabla u) - b(u)u \in \lambda \partial F(x,u)\;\text{ in }\;\Omega , \quad u=0\; \text{ on }\;\partial \Omega \end{aligned}$$ where $$\Omega \subset \mathbb{R }^N$$ is a bounded domain, $$N\ge 2$$ and $$\partial F(x,u)$$ is a generalized gradient of $$F(x,t)$$ with respect to $$t$$ . The main tools utilized are Variational Methods for Locally Lipschitz Functional and a Concentration Compactness Theorem for Orlicz space. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Claudianor Alves & José Gonçalves & Jefferson Santos, 2014. "Strongly nonlinear multivalued elliptic equations on a bounded domain," Journal of Global Optimization, Springer, vol. 58(3), pages 565-593, March.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:3:p:565-593
    DOI: 10.1007/s10898-013-0052-3
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    References listed on IDEAS

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    1. Alexandru Kristály & Waclaw Marzantowicz & Csaba Varga, 2010. "A non-smooth three critical points theorem with applications in differential inclusions," Journal of Global Optimization, Springer, vol. 46(1), pages 49-62, January.
    2. Kaimin Teng, 2010. "Multiple solutions for semilinear resonant elliptic problems with discontinuous nonlinearities via nonsmooth double linking theorem," Journal of Global Optimization, Springer, vol. 46(1), pages 89-110, January.
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    Cited by:

    1. Claudianor O. Alves & Tuhina Mukherjee, 2021. "Existence of solution for a class of elliptic problems in exterior domain with discontinuous nonlinearity," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-32, February.

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