POSITIVE SOLUTION BRANCH FOR ELLIPTIC PROBLEMS WITH CRITICAL INDEFINITE NONLINEARITY

In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely −∆u = λu + h(x)u n+2 n−2 in a smooth domain bounded (respectively, unbounded) Ω ⊆ R n ,n >4, for λ ≥ 0. Under suitable assumptions on the weight function, we obtain the positive solution branch, bifurcating from the first eigenvalue λ1(Ω) (respectively, the bottom of the essential spec- trum).