Existence results for degenerate p(x)-Laplace equations with Leray-Lions type operators

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• 作者：Ky Ho ; Inbo Sim
• 关键词：p(x) ; Laplacian ; weighted variable exponent Lebesgue ; Sobolev spaces ; multiplicity ; a priori bound ; Leray ; Lions type operators
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：60
• 期：1
• 页码：133-146
• 全文大小：263KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.