In this paper we consider the bifurcation problem -div A(x,?u)=λa(x)|u|~(p-2)u+f(x,u,λ) in Ω with p>1.Under some proper assumptions on A(x,ξ),a(x)and f(x,u,λ),we show that the existence of an unbounded branch of positive solutions bifurcating from the principal eigenvalue of...