Lions-type theorem of the fractional Laplacian and applications (Q2047660)

In this paper, the authors study a class of fractional Schrödinger equation \((-\Delta)^su + V(|x|)u = f(u), x\in\mathbb R^N,\) with radially symmetric potential \(V\), and prove a generalized version of Lions-type theorem in the case the nonlinearity \(f\) contains both embedding top and bottom indices. As an application of this theorem, the authors consider the existence of ground state solutions when \(f(u)=|u|^{2^*_s-2}u +\lambda |u|^{q-2}u + |u|^{2^*_{\alpha,s}-2}u,\) and \(2^*_{\alpha,s}=2+\frac{2\alpha}{N-2s}, \alpha\in(0,2s)\).