Constrained Minimizers of the Fourth-Order Schrodinger Equation With Saturable Nonlinearity

In this paper, we consider the existence of normalized solutions for the following fourth-order Schr & ouml;dinger equation with saturated nonlinearity: {Delta(2)u-Delta u+lambda u=mu I(x)+u(2) /1+I(x)+u(2)u, x is an element of R-N integral(RN)|u|(2)dx=a(2), where N >= 2,lambda is an element of R,mu>0, and I(x)is an element of C(R-N,R) is a bounded function. We prove that there exists mu 1>0, such that the fourth-order Schrodinger equation admits a radial ground-state normalized solution (u,lambda) if mu>mu 1. Furthermore, we obtain that the estimates of upper bound for the ground-state energy and the upper and lower bounds for the Lagrange multiplier lambda.