Normalized ground state of a mixed dispersion nonlinear Schrodinger equation with combined power-type nonlinearities

Abstract

We study the existence of normalized ground state solutions to a mixed dispersion fourth-order nonlinear Schrodinger equation with combined power-type nonlinearities. By analyzing the subadditivity of the ground state energy with respect to the prescribed mass, we employ a constrained minimization method to establish the existence of ground state that corresponds to a local minimum of the associated functional. Under certain conditions, by studying the monotonicity of ground state energy as the mass varies, we apply the constrained minimization arguments on the Nehari-Pohozaev manifold to prove the existence of normalized ground state solutions. For more information see https://ejde.math.txstate.edu/Volumes/2024/29/abstr.html