Positive solutions of generalized nonlinear logistic equations via sub-super solutions

Abstract

Let Ω be a smooth bounded domain in RN, N≥1, let m,n be two nonnegative functions defined in Ω and let ϕ:RN→RN be a continuous and strictly monotone mapping. We consider the existence and nonexistence of positive solutions for nonlinear problems involving the ϕ-Laplacian, of the form {−divϕ(∇u)=λm(x)f(u)−n(x)g(u)in Ω,u=0on ∂Ω where λ>0 is a real parameter, and f,g:[0,∞)→[0,∞) are continuous functions modeled by f(t)=tq and g(t)=tr with 0