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Open Access Research

Existence of positive solutions of elliptic mixed boundary value problem

Guofa Li

Author Affiliations

Department of Mathematics and Information Science, Qujing Normal University, Qujing, 655011, P.R. China

Boundary Value Problems 2012, 2012:91  doi:10.1186/1687-2770-2012-91

Published: 16 August 2012

Abstract

In this paper, we use variational methods to prove two existence of positive solutions of the following mixed boundary value problem:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/91/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/91/mathml/M1">View MathML</a>

One deals with the asymptotic behaviors of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/91/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/91/mathml/M2">View MathML</a> near zero and infinity and the other deals with superlinear of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/91/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/91/mathml/M2">View MathML</a> at infinity.

MSC: 35M12, 35D30.

Keywords:
elliptic mixed boundary value problem; positive solutions; mountain pass theorem; Sobolev embedding theorem