Multiplicity of solutions for a general p(x)-Laplacian Dirichlet problem
Copyright policy )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.
- Mohamed I University Morocco
multiple solutions, 37B30, Multiple solutions, Variational method, p(x)-Laplace operator, weak solution, Ambrosetti-Rabinowitz condition, nonlinear Dirichlet problems, Sobolev space, \(p(x)\)-Laplace operator, variational method, Generalized Lebesgue–Sobolev spaces, mountain pass theorem, 35A15, Nonlinear boundary value problems for nonlinear elliptic equations, generalized Lebesgue-Sobolev spaces, Weak solutions to PDEs, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Quasilinear elliptic equations with \(p\)-Laplacian
multiple solutions, 37B30, Multiple solutions, Variational method, p(x)-Laplace operator, weak solution, Ambrosetti-Rabinowitz condition, nonlinear Dirichlet problems, Sobolev space, \(p(x)\)-Laplace operator, variational method, Generalized Lebesgue–Sobolev spaces, mountain pass theorem, 35A15, Nonlinear boundary value problems for nonlinear elliptic equations, generalized Lebesgue-Sobolev spaces, Weak solutions to PDEs, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Quasilinear elliptic equations with \(p\)-Laplacian
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