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

Abstract

This paper is devoted to studying the following nonlinear biharmonic Schrödinger equation with combined power-type nonlinearities Δ2u−λu=μ|u|q−2u+|u|4∗−2uinRN,where N≥5, μ>0, 2<q<2+8N, 4∗=2NN−4 is the H2-critical Sobolev exponent, and λ 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.