A multiplicity theorem for parametric superlinear (p,q)-equations | Zendy

Florin-Iulian Onete | Zendy; Nikolaos S. Papageorgiou | Zendy; Calogero Vetro | Zendy

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A multiplicity theorem for parametric superlinear (p,q)-equations

Author(s) -

Florin-Iulian Onete,

Nikolaos S. Papageorgiou,

Calogero Vetro

Publication year - 2020

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2020.40.1.131

Subject(s) - mathematics , mountain pass theorem , truncation (statistics) , multiplicity (mathematics) , parametric statistics , nonlinear system , laplace operator , term (time) , mathematical analysis , combinatorics , pure mathematics , discrete mathematics , statistics , physics , quantum mechanics

We consider a parametric nonlinear Robin problem driven by the sum of a p-Laplacian and of a q-Laplacian ((p, q)-equation). The reaction term is (p − 1)-superlinear but need not satisfy the Ambrosetti–Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

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