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

Νικόλαος Παπαγεωργίου | Zendy; Calogero Vetro | Zendy; Francesca Vetro | Zendy

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

Author(s) -

Νικόλαος Παπαγεωργίου,

Calogero Vetro,

Francesca Vetro

Publication year - 2018

Publication title -

opuscula mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 16

eISSN - 2300-6919

pISSN - 1232-9274

DOI - 10.7494/opmath.2019.39.2.227

Subject(s) - mathematics , lambda , type (biology) , bifurcation , parametric statistics , nonlinear system , logistic function , combinatorics , laplace operator , set (abstract data type) , p laplacian , term (time) , mathematical analysis , pure mathematics , statistics , physics , ecology , quantum mechanics , optics , boundary value problem , biology , computer science , programming language

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.

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