On existence of normalized solutions to some classes of elliptic problems with L2-supercritical growth

Abstract

In this paper, we present a new approach that can be used to prove the existence of normalized solution for elliptic problems with nonlinearity having an $L^2$-supercritical growth, where the domain can be bounded, the whole $R^N$ or the Half space $R_{+}^N$. Moreover, this method also makes the studies of normalized solutions for problem involving magnetic field available.