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

Opuscula Mathematica

卷:39

Nikolaos S. Papageorgiou¹  Francesca Vetro²  Calogero Vetro³ 

[1] National Technical University, Department of Mathematics, Zografou Campus, 15780, Athens, Greece;

[2] Nonlinear Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;

[3] University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123, Palermo, Italy;

关键词: positive solutions;    superdiffusive reaction;    local minimizers;    maximum principle;    minimal positive solutions;    robin boundary condition;    indefinite potential;   

DOI  :  https://doi.org/10.7494/OpMath.2019.39.2.227

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown