Positive solution branch for elliptic problems with critical indefinite nonlinearity. (Q976622)

The semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely \(-\Delta u=\lambda u+h(x)u^{\frac {n+2}{n-2}}\) in a smooth domain bounded (respectively, unbounded) \(\Omega \subseteq \mathbb R^n\), \(n>4\), for \(\lambda \geq 0\) is studied. Under suitable assumptions on the weight function, the positive solution branch, bifurcating from the first eigenvalue \(\lambda _1(\Omega)\) (respectively, the bottom of the essential spectrum) is obtained.