Abstract
This paper investigates the existence and multiplicity of solutions for superlinear \(p(x)\)-Laplacian equations with Dirichlet boundary conditions. Under no Ambrosetti–Rabinowitz’s superquadraticity conditions, we obtain the existence and multiplicity of solutions using a variant Fountain theorem without Palais-Smale type assumptions.
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The author would like to thank Prof. Dr. R.A. Mashiyev for his generous advice and support.
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Communicated by Syakila Ahmad.
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Yucedag, Z. Existence of Solutions for \(p(x)\) Laplacian Equations Without Ambrosetti–Rabinowitz Type Condition. Bull. Malays. Math. Sci. Soc. 38, 1023–1033 (2015). https://doi.org/10.1007/s40840-014-0057-1
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DOI: https://doi.org/10.1007/s40840-014-0057-1
Keywords
- \(p(x)\)-Laplace operator
- Variable exponent Lebesgue–Sobolev spaces
- Variational approach
- Variant fountain theorem