Infinitely many large solutions to a variable order nonlocal singular equation

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作者
Sekhar Ghosh
Dumitru Motreanu
机构
[1] Indian Statistical Institute Bangalore,Statistics and Mathematics Unit
[2] National Institute of Technology Rourkela,Department of Mathematics
[3] Université de Perpignan,Département de Mathématiques
关键词
Fractional ; -Laplacian; Singularity (primary); Variable order fractional Sobolev space; Symmetric mountain pass theorem; Truncation; 35R11; 35J75 primary; 35J60; 46E35;
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摘要
The paper establishes the existence of infinitely many large energy solutions for a nonlocal elliptic problem involving a variable exponent fractional p(·)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(\cdot )$$\end{document}-Laplacian and a singularity, provided a positive parameter incorporated in the problem is sufficiently small. A variational method can be implemented for an associated problem obtained by truncation related to the singularity. A comparison argument allows one to pass to the original singular problem.
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页码:822 / 839
页数:17
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