(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

Calogero Vetro; Nikolaos S. Papageorgiou

(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

Calogero Vetro, Nikolaos S. Papageorgiou

Matematica e Informatica

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

5 Citations (Scopus)

Abstract

We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian (p> 2) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric (p- 1) -linear term which is resonant as x→ - ∞, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.

Original language	English
Pages (from-to)	221-251
Number of pages	31
Journal	Applied Mathematics and Optimization
Volume	81
Publication status	Published - 2020

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics

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title = "(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms",

abstract = "We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian (p> 2) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric (p- 1) -linear term which is resonant as x→ - ∞, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.",

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

year = "2020",

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pages = "221--251",

journal = "Applied Mathematics and Optimization",

issn = "0095-4616",

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T1 - (p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

AU - Vetro, Calogero

AU - Papageorgiou, Nikolaos S.

PY - 2020

Y1 - 2020

N2 - We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian (p> 2) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric (p- 1) -linear term which is resonant as x→ - ∞, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.

AB - We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian (p> 2) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric (p- 1) -linear term which is resonant as x→ - ∞, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.

UR - http://hdl.handle.net/10447/400184

UR - https://link.springer.com/article/10.1007/s00245-018-9482-0

M3 - Article

VL - 81

SP - 221

EP - 251

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

SN - 0095-4616

ER -