SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Existence of an unbounded branch of the set of solutions for equations of p(x)-Laplace type

Yun-Ho Kim

Author Affiliations

Department of Mathematics Education, Sangmyung University, Seoul, 110-743, Republic of Korea

Boundary Value Problems 2014, 2014:27  doi:10.1186/1687-2770-2014-27

Published: 30 January 2014

Abstract

We are concerned with the following nonlinear problem

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/27/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/27/mathml/M2">View MathML</a>

subject to Dirichlet boundary conditions, provided that μ is not an eigenvalue of the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/27/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/27/mathml/M1">View MathML</a>-Laplacian. The purpose of this paper is to study the global behavior of the set of solutions for nonlinear equations of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/27/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/27/mathml/M1">View MathML</a>-Laplacian type by applying a bifurcation result for nonlinear operator equations.

MSC: 35B32, 35D30, 35J60, 35P30, 37K50, 46E35, 47J10.

Keywords:
<a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/27/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/27/mathml/M1">View MathML</a>-Laplacian; variable exponent Lebesgue-Sobolev spaces; weak solution; eigenvalue