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

Calogero Vetro; Francesca Vetro; Nikolaos S. Papageorgiou

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

Calogero Vetro, Francesca Vetro, Nikolaos S. Papageorgiou

Matematica e Informatica

Research output: Contribution to journal › Article › peer-review

10 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 language	English
Pages (from-to)	347-374
Number of pages	28
Journal	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S
Volume	12
Publication status	Published - 2019

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

@article{61e2e1907d1c496188e228c196832f38,

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

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.",

author = "Calogero Vetro and Francesca Vetro and Papageorgiou, {Nikolaos S.}",

year = "2019",

language = "English",

volume = "12",

pages = "347--374",

journal = "Discrete and Continuous Dynamical Systems - Series S",

issn = "1937-1632",

publisher = "American Institute of Mathematical Sciences",

}

TY - JOUR

T1 - Multiple solutions for (p,2)-equations at resonance

AU - Vetro, Calogero

AU - Vetro, Francesca

AU - Papageorgiou, Nikolaos S.

PY - 2019

Y1 - 2019

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.

AB - 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.

UR - http://hdl.handle.net/10447/334782

UR - http://aimsciences.org/article/doi/10.3934/dcdss.2019024

M3 - Article

VL - 12

SP - 347

EP - 374

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

SN - 1937-1632

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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