Constrained Minimizers of the Fourth‐Order Schrödinger Equation With Saturable Nonlinearity

ABSTRACT

In this paper, we consider the existence of normalized solutions for the following fourth‐order Schrödinger equation with saturated nonlinearity: , where , and is a bounded function. We prove that there exists , such that the fourth‐order Schrödinger equation admits a radial ground‐state normalized solution if . Furthermore, we obtain that the estimates of upper bound for the ground‐state energy and the upper and lower bounds for the Lagrange multiplier .