On generalized logistic equations with a non-homogeneous differential operator

Abstract

We consider a generalized logistic equation of superdiffusive type, driven by a non-homogeneous nonlinear differential operator, which incorporates the p-Laplacian, the (p, q)-differential operator and the generalized p-mean curvature differential operator. Using variational methods coupled with truncation and comparison techniques, we prove a bifurcation-type theorem describing the dependence of positive solutions on the parameter λ > 0.