Open Access Research

Infinitely many solutions for a class of quasilinear elliptic equations with p-Laplacian in R N

Gao Jia*, Jie Chen and Long-jie Zhang

Author Affiliations

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

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Boundary Value Problems 2013, 2013:179  doi:10.1186/1687-2770-2013-179

Published: 6 August 2013

Abstract

In this paper, we study the multiplicity of solutions for a class of quasilinear elliptic equations with p-Laplacian in <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/179/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/179/mathml/M1">View MathML</a>. In this case, the functional J is not differentiable. Hence, it is difficult to work under the classical framework of the critical point theory. To overcome this difficulty, we use a nonsmooth critical point theory, which provides the existence of critical points for nondifferentiable functionals.

MSC: 35J20, 35J92, 58E05.

Keywords:
quasilinear elliptic equations; nondifferentiable functional; p-Laplacian; multiple solutions