Constant sign and nodal solutions for nonlinear robin equations with locally defined source term

Calogero Vetro, Francesca Vetro, Nikolaos S. Papageorgiou

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).
Original languageEnglish
Pages (from-to)374-390
Number of pages17
JournalMathematical Modelling and Analysis
Volume25
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modelling and Simulation

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