On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104811We consider a class of nonlinear Dirichlet problems involving the $p(x)$--Laplace operator. Our framework is based on the theory of Sobolev spaces with variable exponent and we establish the existence of a weak solution in such a space. The proof relies on the Mountain Pass Theorem.Analysis of PDEsMathematical Physics35D05, 35J60, 35P30, 47H15, 58E05On a nonlinear eigenvalue problem in Sobolev spaces with variable exponenttext