Existence Theorems for Some Classes of Boundary Value Problems Involving the P(X)-Laplacian - Andrei, Ionica (Nonlinear Analysis: Modelling and Control, 2008)
We prove an alternative for a nonlinear eigenvalue problem involving the p(x)-Laplacian and study a subcritical boundary value problem for the same operator. The theoretical approach is the Mountain Pass Lemma and one of its variants, which is very useful in the study of eigenvalue problems.
Keywords: p(x)-Laplacian; nonlinear eigenvalue problem; critical point theory