Three solutions to a class of $p(x)$-Laplace equation based on Nehari skill

Liu Duchao

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Three solutions to a class of $p(x)$-Laplace equation based on Nehari skill

Liu Duchao *

School of mathematical and statistic of Lanzhou University

*Correspondence author

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Funding: none

Opened online: 5 September 2008

Accepted by: none

Citation: Liu Duchao .Three solutions to a class of $p(x)$-Laplace equation based on Nehari skill[OL]. [ 5 September 2008] http://en.paper.edu.cn/en_releasepaper/content/23823

In this paper, we show the existence of at least three nontrivial solutions to the quasilinear elliptic equation-p(x)-Laplacian equation in a smooth bounded domain with nonlinear boundary condition or Dirichlet boundary condition u=0. The method we used here is based on Nehari skills on three sub-manifolds of the space W^{1,p(x)}(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\Omega).

Keywords:Critical points; $p(x)$-Laplacian; Integral functional; Generalized Lebesgue-Sobolev spaces

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