Fractional Schrödinger equation in bounded domains and applications (Q1679174)

The main purpose of the paper is the study of the positive solutions to a fractional Schrödinger problem. Precisely, for a nontrivial measure \(\mu\), the author shows that the considered problem admits one and only one solution \(u \in C^+\). The second purpose is to present some new results on the semilinear equation \(\Delta^{(\alpha/2)}u=u^\gamma\) on \(B\) (\(B\) being the unit ball in \(\mathbb R^d\)), which are closely related to the above problem. This second part is a continuation of the recent work by the author and Ben Fredj.