This paper is motivated by a gauged Schrödinger equation in dimension 2 including the so-called Chern-Simons term. The study of radial stationary states leads to the nonlocal problem:
This problem is the Euler-Lagrange equation of a certain energy functional. In this paper the study of the global behavior of such functional is completed. We show that for , the functional may be bounded from below or not, depending on . Quite surprisingly, the threshold value for is explicit. From this study we prove existence and non-existence of positive solutions.
Cite this article
Alessio Pomponio, David Ruiz, A variational analysis of a gauged nonlinear Schrödinger equation. J. Eur. Math. Soc. 17 (2015), no. 6, pp. 1463–1486DOI 10.4171/JEMS/535