Positive Solution for the Elliptic Problems with Sublinear and Superlinear Nonlinearities

Abstract

This paper deals with the existence of positive solutions for the elliptic problems with sublinear and superlinear nonlinearities-Δu=λa(x)up+b(x)uqinΩ,u>0inΩ,u=0on∂Ω, whereλ>0is a real parameter,0<p<1<q.Ωis a bounded domain inRN  (N≥3), anda(x)andb(x)are some given functions. By means of variational method and super-subsolution method, we obtain some results about existence of positive solutions.