Opuscula Math. 39, no. 2 (2019), 227-245

Opuscula Mathematica

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

Nikolaos S. Papageorgiou
Calogero Vetro
Francesca Vetro

Abstract. 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 of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter \(\lambda \gt 0\) varies. Also, we show that for every admissible parameter \(\lambda \gt 0\), the problem admits a smallest positive solution.

Keywords: positive solutions, superdiffusive reaction, local minimizers, maximum principle, minimal positive solutions, Robin boundary condition, indefinite potential.

Mathematics Subject Classification: 35J20, 35J60.

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  • Nikolaos S. Papageorgiou
  • National Technical University, Department of Mathematics, Zografou Campus, 15780, Athens, Greece
  • Communicated by Giovanni Molica Bisci.
  • Received: 2018-04-25.
  • Revised: 2018-11-07.
  • Accepted: 2018-11-07.
  • Published online: 2018-12-07.
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Cite this article as:
Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro, On a Robin (p,q)-equation with a logistic reaction, Opuscula Math. 39, no. 2 (2019), 227-245, https://doi.org/10.7494/OpMath.2019.39.2.227

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