Abstract
In this paper, we study the multiplicity of solutions for a class of quasilinear elliptic equations with p-Laplacian in . 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.
Highlights
Introduction and main resultsRecently, the multiplicity of solutions for the quasilinear elliptic equations has been studied extensively, and many fruitful results have been obtained
Liu considered the existence of multiple nonzero solutions of the Dirichlet boundary value problem
In order to determine weak solutions of ( . ) in a suitable functional space E, we look for critical points of the functional J : E → R defined by
Summary
The multiplicity of solutions for the quasilinear elliptic equations has been studied extensively, and many fruitful results have been obtained. B(x) – λ u = f (x, u), in RN , and proved the multiplicity of solutions of the problem ) by using the nonsmooth critical point theory. We shall investigate the existence of infinitely many solutions of the following problem. ) is based on the nonsmooth critical point theory developed in [ ] and [ ]. Dealing with this class of problems, the main difficulty is that the associated functional is not differentiable in all directions. To state and prove our main result, we consider the following assumptions
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