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
RivistaDefault journal
Volume11
Stato di pubblicazionePublished - 2018

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Multiple Solutions
Smooth Solution
Critical Group
Nodal Solutions
Principal Eigenvalue
Morse Theory
P-Laplacian
Strengthening
Variational Methods
Truncation
Dirichlet Problem
Regularity
Zero
Term

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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Multiple solutions for nonlinear nonhomogeneous resonant coercive problems. / Averna, Diego; Tornatore, Elisabetta; Papageorgiou, Nikolaos S.

In: Default journal, Vol. 11, 2018, pag. 155-178.

Risultato della ricerca: Article

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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.",
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T1 - Multiple solutions for nonlinear nonhomogeneous resonant coercive problems

AU - Averna, Diego

AU - Tornatore, Elisabetta

AU - Papageorgiou, Nikolaos S.

PY - 2018

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N2 - 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.

AB - 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.

KW - Analysis

KW - Applied Mathematics

KW - Constant sign and nodal solutions

KW - Critical groups

KW - Discrete Mathematics and Combinatorics

KW - Extremal constant sign solutions

KW - Multiple smooth solutions

KW - Nonlinear regularity

KW - Resonance

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M3 - Article

VL - 11

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JO - Default journal

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