Positive solution branch for elliptic problems with critical indefinite nonlinearity.

Jyotshana Prajapat University of Alabama at Birmingham, USA

We study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely −Δu = λu + h(x)u^{\frac{n+2}{n−2}} in a smooth, bounded (respectively unbounded) domain 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 λ_{1}(Ω) (respectively, the bottom of the essential spectrum).