Normalized ground states of nonlinear biharmonic Schrodinger equations with Sobolev critical growth and combined nonlinearities

This paper is devoted to studying the following nonlinear biharmonic Schrodinger equation with combined power-type nonlinearities delta 2u - lambda u = mu|u|q-2u + |u|4*-2u in R-N, where N > 5, mu > 0, 2 < q < 2+ 8N, 4* = 2N/N-4 is the H2-critical Sobolev exponent, and lambda appears as a Lagrange multiplier. By analyzing the behavior of the ground state energy with respect to the prescribed mass, we establish the existence of normalized ground state solutions. Furthermore, all ground states are proved to be local minima of the associated energy functional.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the nonlinear biharmonic Schrödinger equation with combined power-type nonlinearities in R-N space. By analyzing the behavior of the ground state energy with respect to the prescribed mass, the existence of normalized ground state solutions is established. Furthermore, it is proven that all ground states are local minima of the associated energy functional.