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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.

Superlinear Robin problems with indefinite linear part

Gasiński L., Papageorgiou N. S.

Science, Technology and Innovation

2018

Vol. 2, no. 1

74--94

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a superlinear reaction term which need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools we prove two theorems. An existence theorem producing a nontrivial smooth solution and a multiplicity theorem producing a whole unbounded sequence of nontrivial smooth solutions.