Critical singular problems on unbounded domains

Abstract

We present some results of existence for the following problem: $-\Delta u=a\left(x\right)g\left(u\right)+u{\left|u\right|}^{2\ast -2}$, $x\in {ℝ}^N\left(N\ge 3\right)$, $u\in D^{1,2}\left({ℝ}^N\right)$, where the function $a$ is a sign-changing function with a singularity at the origin and $g$ has growth up to the Sobolev critical exponent $2^{\ast }=2N/\left(N-2\right)$.