This article shows the existence of at least three nontrivial solutions to the quasilinear elliptic equation
in a smooth bounded domain , with the nonlinear boundary condition or the Dirichlet boundary condition on . In addition, this paper proves that one solution is positive, one is negative, and the last one is a sign-changing solution. The method used here is based on Nehari results, on three sub-manifolds of the space .
Submitted September 26, 2008. Published March 3, 2010.
Math Subject Classifications: 35B38, 35D05, 35J20.
Key Words: Critical points; p(x)-Laplacian; integral functionals; generalized Lebesgue-Sobolev spaces.
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| Duchao Liu |
School of Mathematics and Statistics
Lanzhou University, Lanzhou 730000, China
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