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On the Solvability of Superlinear and Nonhomogeneous Quasilinear Equations

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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Correspondence to Gao Jia.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Jia, G., Zhao, Q. & Dai, Cy. On the Solvability of Superlinear and Nonhomogeneous Quasilinear Equations. Bound Value Probl 2009, 156063 (2009). https://doi.org/10.1155/2009/156063

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Weak Solution
  • Functional Equation
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