Multiple solutions for nonlinear nonhomogeneous resonant coercive problems

Diego Averna, Elisabetta Tornatore, Nikolaos S. Papageorgiou

Risultato della ricerca: Article

2 Citazioni (Scopus)

Abstract

We consider a nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian (2 < p) and a Laplacian. The reaction term is a Caratheodory function f(z, x) which is resonant with respect to the principal eigenvalue of (- ∆_p, W_0^{1,p}(Ω)). Using variational methods combined with truncation and comparison techniques and Morse theory (critical groups) we prove the existence of three nontrivial smooth solutions all with sign information and under three different conditions concerning the behavior of f(z, ·) near zero. By strengthening the regularity of f(z, ·), we are able to generate a second nodal solution for a total of four nontrivial smooth solutions.
Lingua originaleEnglish
pagine (da-a)155-178
Numero di pagine24
RivistaDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S
Volume11
Stato di pubblicazionePublished - 2018

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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