Existence and asymptotic behavior of ground states for Choquard-Pekar equations with Hardy potential and critical reaction (Q2117509)

This article discusses the existence and asymptotic behavior of ground state solutions for a nonautonomous Choquard-Pekar equation \[ -\Delta u+\Big(K(x)-\frac{\mu}{|x|^2|}\Big) u=(W\ast F(u))f(u)+|u|^{2^*-2}u\quad\mbox{ in }\mathbb{R^N}\setminus\{0\}. \] Where \(N\geq 3\), \(\mu<(N-2)^2/4\), \(2^*=2N/(N-2)\) and \(K\) is allowed to change sign. Under some structural conditions on \(W\) the authors obtain the existence of ground state solutions. It is further shown that as \(\mu\to 0^+\) these ground state solutions converge (up to a \(\mathbb{Z}^N\)-translation) to a ground state solution of the limiting problem.