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MiS Preprint
89/2013

Multiple Solutions for Semi-linear Corner Degenerate Elliptic Equations

Hua Chen, Xiaochun Liu and Yawei Wei

Abstract

The present paper is concerned with the existence of multiple solutions for semi-linear corner-degenerate elliptic equations with subcritical conditions. First, we introduce the corner type weighted p-Sobolev spaces and discuss the properties of continuous embedding, compactness and spectrum. Then, we prove the corner type Sobolev inequality and Poincaré inequality, which are important in the proof of the main result.

Received:
Aug 19, 2013
Published:
Aug 19, 2013
Keywords:
dirichlet problem, multiple solutions, corner-degenerate elliptic operators, corner type weighted p-Sobolev spaces, corner type Sobolev inequality

Related publications

inJournal
2014 Repository Open Access
Hua Chen, Xiaochun Liu and Yawei Wei

Multiple solutions for semi-linear corner degenerate elliptic equations

In: Journal of functional analysis, 266 (2014) 6, pp. 3815-3839