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Positive solutions for nonlinear Robin problems with conviction

Gasiński Leszek, Papageorgiou Nikolaos S.

Science, Technology and Innovation

2021

Vol. 12, no. 1

23--36

We consider a Robin problem driven by the p-Laplacian and with a reaction which is gradient dependent (convection). Using truncations and perturbations, we show that the problem has at least one positive smooth solution.

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.