Infinitely many solutions for a differential inclusion problem in ℝN

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Abstract

In this paper we consider the differential inclusion problem -△pu + u p-2u ∈ α(x)∂F(u(x)), x ∈ ℝN, u ∈ W1,p(ℝN), where 2 ≤ N < p < + ∞, α ∈ L1(ℝN) ∩ L (ℝN) is radially symmetric, and ∂F stands for the generalized gradient of a locally Lipschitz function F : ℝ → ℝ. Under suitable oscillatory assumptions on the potential F at zero or at infinity, we show the existence of infinitely many, radially symmetric solutions of (DI). No symmetry requirement on F is needed. Our approach is based on a non-smooth Ricceri-type variational principle, developed by Marano and Motreanu (J. Differential Equations 182 (2002) 108-120).

Original languageEnglish
Pages (from-to)511-530
Number of pages20
JournalJournal of Differential Equations
Volume220
Issue number2
DOIs
Publication statusPublished - Jan 15 2006

Keywords

  • Critical point
  • Differential inclusion
  • Generalized gradient
  • Locally Lipschitz function
  • Ricceri's variational principle
  • p-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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