Nonsmooth Neumann-type problems involving the p-Laplacian

Alexandru Kristály, Dumitru Motreanu

Research output: Contribution to journalArticle

7 Citations (Scopus)


This paper deals with the problem-pu+(x)|u|p-2u=(x)f(|u|) in , subjected to the zero Neumann boundary condition, where p1, N is bounded with smooth boundary, , L(), essinf0, and f:[0,+) is a not necessarily continuous nonlinearity that oscillates either at the origin or at the infinity. By using nonsmooth variational methods, we establish in both cases the existence of infinitely many distinct non-negative solutions of the Neumann problem. In our framework, : may be a sign-changing or even a nonpositive potential, which is not permitted usually in earlier works.

Original languageEnglish
Pages (from-to)1309-1326
Number of pages18
JournalNumerical Functional Analysis and Optimization
Issue number11-12
Publication statusPublished - Nov 2007


  • Infinitely many solutions
  • Neumann problem
  • Nonsmooth potential
  • P-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

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