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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

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.