Existence of Solutions for \(p(x)\) Laplacian Equations Without Ambrosetti–

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• 作者：Zehra Yucedag
• 关键词：$$p(x)$$ p ( x ) ; Laplace operator ; Variable exponent Lebesgue–Sobolev spaces ; Variational approach ; Variant fountain theorem ; 35D05 ; 35J60 ; 35J70
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：38
• 期：3
• 页码：1023-1033
• 全文大小：438 KB
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• 作者单位：Zehra Yucedag (1)
  
  1. Department of Mathematics, Faculty of Science, Dicle University, 21280, Diyarbakir, Turkey
  
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206

文摘

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. Keywords \(p(x)\)-Laplace operator Variable exponent Lebesgue–Sobolev spaces Variational approach Variant fountain theorem