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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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
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

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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.",
keywords = "Constant sign and nodal solutions; Critical groups; Extremal constant sign solutions; Multiple smooth solutions; Nonlinear regularity; Resonance; Analysis; Discrete Mathematics and Combinatorics; Applied Mathematics",
author = "Diego Averna and Elisabetta Tornatore and Papageorgiou, {Nikolaos S.}",
year = "2018",
language = "English",
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pages = "155--178",
journal = "DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S",
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TY - JOUR

T1 - Multiple solutions for nonlinear nonhomogeneous resonant coercive problems

AU - Averna, Diego

AU - Tornatore, Elisabetta

AU - Papageorgiou, Nikolaos S.

PY - 2018

Y1 - 2018

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 - Constant sign and nodal solutions; Critical groups; Extremal constant sign solutions; Multiple smooth solutions; Nonlinear regularity; Resonance; Analysis; Discrete Mathematics and Combinatorics; Applied Mathematics

UR - http://hdl.handle.net/10447/265013

UR - http://aimsciences.org/journals/pdfs.jsp?paperID=14664&mode=full

M3 - Article

VL - 11

SP - 155

EP - 178

JO - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S

JF - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S

SN - 1937-1632

ER -