Critical singular problems on unbounded domains (Q2495028)

Summary: We present some existence results for the following problem: \(-\Delta u=a(x)g(u)+u|u|^{2*-2}, x\in{\mathbb R}^N (N\geq3),\;u\in D^{1,2}({\mathbb R}^N)\), 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 \(2^*=2N/(N-2)\).