Normalized ground state solutions of the biharmonic Schrödinger equation with general mass supercritical nonlinearities

Abstract

We are interested in the following problem $\left(\begin{array}{c}{\Delta }^{2}u+\lambda u=g\left(u\right)\text{in}{R}^N,\\ {\int }_{R^N}{\left|u\right|}^{2}dx=c,\end{array}\right)$where $N\ge 5$, $c>0$ and $\lambda \in R$ appears as a Lagrange multiplier. When $g\left(u\right)$ satisfies a class of general mass supercritical conditions, we introduce one more constraint and consider the corresponding infimum. After showing that the new constraint is natural and verifying the compactness of the minimizing sequence, we obtain the existence of normalized ground state solutions. In this sense, the existing results are generalized and improved significantly.