POSITIVE SOLUTIONS FOR ELLIPTIC PROBLEMS WITH CRITICAL INDEFINITE NONLINEARITY IN BOUNDED DOMAINS

In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely u = u + h(x)u (n+2)/(n 2) in a smooth open bounded domain R n , n > 4 with Dirichlet boundary conditions and for 0. Under suitable assumptions on the weight function, we obtain the positive solution branch, bifurcating from the first eigenvalue 1(). For n = 2, we get similar results for u = u + h(x) (u)e u where is bounded and superlinear near zero.