Sharp non-existence results of prescribed L^2-norm solutions for some class of Schrödinger-Poisson and quasilinear equations

Louis Jeanjean, Tingjian Luo

In this paper we study the existence of minimizers for $$ F(u) = \1/2\int_{\R^3} |\nabla u|^2 dx + 1/4\int_{\R^3}\int_{\R^3}\frac{| u(x) |^2| u(y) |^2}{| x-y |}dxdy-\frac{1}{p}\int…