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Existence Theorems for a Class of Edge-Degenerate Elliptic Equations on Singular Manifolds

Part of: Partial differential equations on manifolds; differential operators Elliptic equations and systems

Published online by Cambridge University Press:  17 February 2015

Haining Fan
Haining Fan*
Affiliation:
School of Sciences, China University of Mining and Technology, Xuzhou 221116, People's Republic of China School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People's Republic of China, (fanhaining888@163.com)
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Abstract

In this paper we establish the Nehari manifold on edge Sobolev spaces and study some of their properties. Furthermore, we use these results and the mountain pass theorem to get non-negative solutions of a class of edge-degenerate elliptic equations on singular manifolds under different conditions.

Keywords

Nehari manifoldsingular manifoldsedge-degenerate

MSC classification

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 58J05: Elliptic equations on manifolds, general theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 2 , June 2015 , pp. 355 - 377
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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