Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 29, pp. 1-20.

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

Authors: Zhouji Ma (Northeast Normal Univ., Changchun, Jilin, China)
         Xiaojun Chang (Northeast Normal Univ., Changchun, Jilin, China)
         Zhaosheng Feng (Univ. of Texas Rio Grande Valley, Edinburg, TX, USA) 

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.

Submitted November 18, 2023. Published April 01, 2024
Math Subject Classifications: 35Q55, 31B30, 35J30.
Key Words: Normalized solutions; Schrodinger equation; Lagrange multiplier; ground states; Nehari-Pohozaev manifold.