The Existence Of Two Solutions For A Perturbed P(x)-Laplacian Equation

In this master thesis,we consider the following Dirichlet problem of p(x)-Laplacian with perturbed term h(x)(?) where p1,p ∈C(Ω)∩ L+∞°(Ω),and p1->p+.By virtue of Nehari manifold method we prove that when h(x)≠0,the problem has two non-trivial solutions which arise form the perturbation of zero solution and a nontrivial solution of the equation for h(x)=0.