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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Multiple Solutions for Semi-linear Corner Degenerate Elliptic Equations
Hua Chen, Xiaochun Liu and Yawei WeiAbstract
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:
- 19.08.13
- Published:
- 19.08.13
- Keywords:
- dirichlet problem, multiple solutions, corner-degenerate elliptic operators, corner type weighted p-Sobolev spaces, corner type Sobolev inequality