Global bifurcation for a class of degenerate elliptic equations with variable exponents

Yun-Ho Kim; Lihe Wang; Chao Zhang

doi:10.1016/j.jmaa.2010.05.058

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Global bifurcation for a class of degenerate elliptic equations with variable exponents

Journal article

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Global bifurcation for a class of degenerate elliptic equations with variable exponents

Yun-Ho Kim, Lihe Wang and Chao Zhang

Journal of mathematical analysis and applications, Vol.371(2), pp.624-637

2010

DOI: 10.1016/j.jmaa.2010.05.058

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Abstract

We are concerned with the following nonlinear problem − div ( w ( x ) | ∇ u | p ( x ) − 2 ∇ u ) = μ g ( x ) | u | p ( x ) − 2 u + f ( λ , x , u , ∇ u ) in Ω subject to Dirichlet boundary conditions, provided that μ is not an eigenvalue of the above divergence form. The purpose of this paper is to study the global behavior of the set of solutions for the above equation, by applying a bifurcation result for nonlinear operator equations.

Bifurcation

Weighted variable exponent Lebesgue–Sobolev spaces

[formula omitted]-Laplacian

Details

Title: Subtitle: Global bifurcation for a class of degenerate elliptic equations with variable exponents
Creators: Yun-Ho Kim - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Lihe Wang - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Chao Zhang - LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
Resource Type: Journal article
Publication Details: Journal of mathematical analysis and applications, Vol.371(2), pp.624-637
DOI: 10.1016/j.jmaa.2010.05.058
ISSN: 0022-247X
eISSN: 1096-0813
Publisher: Elsevier Inc
Language: English
Date published: 2010
Academic Unit: Mathematics
Record Identifier: 9984083241302771

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