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

Francesca Vetro, Calogero Vetro, 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 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.
Lingua originaleEnglish
pagine (da-a)347-374
Numero di pagine28
RivistaDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S
Volume12
Stato di pubblicazionePublished - 2019

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Multiple Solutions
Critical Group
Morse Theory
Smooth Solution
P-Laplacian
Truncation
Dirichlet Problem
Eigenvalue
Term

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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Multiple solutions for (p,2)-equations at resonance. / Vetro, Francesca; Vetro, Calogero; Papageorgiou, Nikolaos S.

In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, Vol. 12, 2019, pag. 347-374.

Risultato della ricerca: Article

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N2 - 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.

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