Multiple Solutions for Semi-linear Corner Degenerate Elliptic Equations
Hua Chen, Xiaochun Liu, and Yawei Wei
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Submission date: 19. Aug. 2013
published in: Journal of functional analysis, 266 (2014) 6, p. 3815-3839
DOI number (of the published article): 10.1016/j.jfa.2013.12.012
Keywords and phrases: dirichlet problem, multiple solutions, corner-degenerate elliptic operators, corner type weighted p-Sobolev spaces, corner type Sobolev inequality
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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.