On the logistic equation for the fractional <i>p</i>‐Laplacian
Antonio Iannizzotto, Sunra Mosconi, Nikolaos S. Papageorgiou
Abstract
Abstract We consider a Dirichlet problem for a nonlinear, nonlocal equation driven by the degenerate fractional p ‐Laplacian, with a logistic‐type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove existence and uniqueness of the positive solution when the parameter lies in convenient intervals. In the superdiffusive case, we establish a bifurcation result. A new strong comparison result, of independent interest, plays a crucial role in the proof of such bifurcation result.
Topics & Concepts
MathematicsDegenerate energy levelsUniquenessBifurcationNonlinear systemLogistic functionFractional LaplacianMathematical analysisDirichlet distributionType (biology)Bifurcation theoryPure mathematicsApplied mathematicsStatisticsPhysicsBoundary value problemQuantum mechanicsEcologyBiologyNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis