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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair


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Volume 18, Issue 2

Issues

Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains

Ryuji Kajikiya
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  • Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan
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Published Online: 2017-06-20 | DOI: https://doi.org/10.1515/ans-2017-6023

Abstract

In the present paper, we study the p-Laplace equation in a hollow symmetric bounded domain. Let H and G be closed subgroups of the orthogonal group such that HG. Then we prove the existence of a positive solution which is H-invariant and G-non-invariant. Furthermore, we give several examples of H, G and Ω, and find symmetric and asymmetric solutions.

Keywords: Group Invariant Solution; Least Energy Solution; Positive Solution,Variational Method

MSC 2010: 35J20; 35J25

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About the article


Received: 2017-02-09

Revised: 2017-05-18

Accepted: 2017-05-19

Published Online: 2017-06-20

Published in Print: 2018-04-01


Funding Source: Japan Society for the Promotion of Science

Award identifier / Grant number: 16K05236

This work was supported by JSPS KAKENHI Grant Number 16K05236.


Citation Information: Advanced Nonlinear Studies, Volume 18, Issue 2, Pages 303–321, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2017-6023.

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