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Open Access Research

Existence of solutions for quasilinear elliptic equations with superlinear nonlinearities

Jia Gao*, Huang Lina and Zhang Xiaojuan

Author affiliations

College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

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Citation and License

Boundary Value Problems 2012, 2012:90  doi:10.1186/1687-2770-2012-90

Published: 10 August 2012

Abstract

Working in a weighted Sobolev space, a new result involving superlinear nonlinearities for a quasilinear elliptic boundary value problem in a domain in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/90/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/90/mathml/M1">View MathML</a> is established. The proofs rely on the Galerkin method, Brouwer’s theorem and a new weighted compact Sobolev-type embedding theorem due to V.L. Shapiro.

MSC: 35J25, 35J62, 65L60.

Keywords:
weighted Sobolev space; superlinear; quasilinear elliptic equation