Existence Theorem for a Class of Nonlinear Fourth-order Schr(o)dinger-Kirchhoff-Type Equations

摘要

This paper is concerned with the existence of nontrivial solutions for the following fourth-order equations of Kirchhoff type ｛△2u-(a+b∫IRN|▽u|2dx)△u+,,λV(x)u=f(x,u),x∈IRN,u ∈ H2 (RN),where a,b are positive constants,λ ≥ 1 is a parameter,and the nonlinearity f is either superlinear or sublinear at infinity in u.With the help of the variational methods,we obtain the existence and multiplicity results in the working spaces.