Nonlinear nonhomogeneous logistic equations of superdiffusive type

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 > 0 (bifurcation-type theorem). We also demonstrate the existence of a minimal positive solution u * and determine the monotonicity and continuity properties of the minimal solution map u * .