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

Onete Florin-Iulian, Papageorgiou Nikolaos S., Vetro Calogero

Opuscula Mathematica

2020

Vol. 40, no. 1

131--149

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.

On a Robin (p, q)-equation with a logistic reaction

Papageorgiou Nikolaos S., Vetro Calogero, Vetro Francesca

Opuscula Mathematica

2019

Vol. 39, no. 2

227--245

We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a p-Laplacian and of a q-Laplacian ((p,q)-equation) plus an indefinite potential term and a parametric reaction ol logistic type (superdiffusive case). We prove a bilurcation-type result describing the changes in the set ol positive solutions as the parameter λ > 0 varies. Also, we show that lor every admissible parameter λ > 0, the problem admits a smallest positive solution. Keywords: positive solutions, superdiffusive reaction, local minimizers, maximum principle, min