Positive solution branch for elliptic problems with critical indefinite nonlinearity

Abstract

In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely -Δu=λu+h(x)u^n+2/n-2 in a smooth domain bounded (respectively, unbounded) Ω⊆Rⁿ, 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 spectrum).