Multiple solutions for (p,2)-equations at resonance

Calogero Vetro, Francesca Vetro, Nikolaos S. Papageorgiou

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian and a reaction term which is (p− 1)-linear near ±∞ and resonant with respect to any nonprincipal variational eigenvalue of (−∆p, W01,p(Ω)). Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them.
Original languageEnglish
Pages (from-to)347-374
Number of pages28
JournalDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S
Volume12
Publication statusPublished - 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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