Multiplicity of solutions for a general \(p(x)\)-Laplacian Dirichlet problem
This paper deals with a class of nonlinear Dirichlet problems involving the \(p(x)\)-Laplace operator. The main result establishes a sufficient condition for the existence of a weak solution in a related Sobolev space with variable exponent. Next, assuming that the nonlinear term fulfills the Ambrosetti-Rabinowitz condition, the authors establish the existence of at least two distinct solutions. The proofs use standard arguments, including the mountain pass theorem and variational methods.
scientific article; zbMATH DE number 6220519
scientific article