Multiplicity and bifurcation of positive solutions for nonhomogeneous semilinear elliptic problems

In this paper we consider the following problem"> where λ>0 is a parameter. We assume uniformly on any compact subset of [0,∞), and do not require for all . We prove that there exists +∞>λ*>0 such that ( ) has exactly two positive solutions for λ (0,λ*), no solution for λ>λ*, a unique solution for λ=λ*, (λ*,u*) is a turning point in , and further analyses of the set of positive solutions are made.