Nonlinear nonhomogeneous logistic equations of superdiffusive type

Abstract

We consider a nonlinear logistic equation of superdiffusive type driven by a nonhomogeneous differential operator and a Robin boundary condition. We prove a multiplicity result for positive solutions which is global with respect to the parameter λ > 0 (bifurcation-type theorem). We also demonstrate the existence of a minimal positive solution uλ and determine the monotonicity and continuity properties of the minimal solution map λ → uλ.