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Open Access Research Article

On the Solvability of Superlinear and Nonhomogeneous Quasilinear Equations

Gao Jia*, Qing Zhao and Chun-yan Dai

Author Affiliations

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

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Boundary Value Problems 2009, 2009:156063  doi:10.1155/2009/156063


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2009/1/156063


Received:14 January 2009
Accepted:6 September 2009
Published:27 September 2009

© 2009 The Author(s).

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using Mountain Pass Lemma, we obtain the existence of nontrivial weak solutions for a class of superlinear and nonhomogeneous quasilinear equations. The key factor in this paper is to use the new idea of near p-homogeneity in conjunction with variational techniques to obtain a new multiplicity result for a vast set of nonlinear equations, such as the mean curvature equation and so on.

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