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# Advanced Nonlinear Studies

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Volume 18, Issue 2

# 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 $H⊊G$. 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.

MSC 2010: 35J20; 35J25

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## About the article

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,

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