A bifurcation problem associated to an asymptotically linear function

We study the existence of positive solutions to a two-order semilinear elliptic problem with Dirichlet boundary condition (Pλ)   {                               u=0              on  ∂Ω,-div(c(x)∇u)=λf(u)inΩ,where Ω ⊂ ℝn; n ≥ 2 is a smooth bounded domain; f is a positive, increasing and convex source term and c(x) is a smooth bounded positive function on Q. We also prove the existence of critical value and claim the uniqueness of extremal solutions.