Multiplicity of solutions for a general \(p(x)\)-Laplacian Dirichlet problem (Q375177)
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scientific article; zbMATH DE number 6220519
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiplicity of solutions for a general \(p(x)\)-Laplacian Dirichlet problem |
scientific article; zbMATH DE number 6220519 |
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Multiplicity of solutions for a general \(p(x)\)-Laplacian Dirichlet problem (English)
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28 October 2013
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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.
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\(p(x)\)-Laplace operator
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generalized Lebesgue-Sobolev spaces
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variational method
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multiple solutions
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nonlinear Dirichlet problems
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weak solution
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Sobolev space
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Ambrosetti-Rabinowitz condition
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mountain pass theorem
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