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RESEARCH PRODUCT

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

Calogero VetroFrancesca VetroNikolaos S. Papageorgiou

subject

local minimizersminimal positive solutionsPure mathematicspositive solutionsGeneral MathematicsType (model theory)Lambda01 natural sciencesPositive solutionSet (abstract data type)Maximum principlesuperdiffusive reactionSettore MAT/05 - Analisi Matematicaindefinite potential0101 mathematicsParametric statisticsMathematicsMinimal positive solutionrobin boundary conditionlcsh:T57-57.97010102 general mathematicsRobin boundary conditionTerm (time)010101 applied mathematicsNonlinear systemmaximum principlelcsh:Applied mathematics. Quantitative methodsLocal minimizer

description

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.

yearjournalcountryeditionlanguage
2019-01-01Opuscula Mathematica
https://doi.org/10.7494/opmath.2019.39.2.227