Open Access Research

Existence of positive solutions of elliptic mixed boundary value problem

Guofa Li

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

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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