4阶非线性薛定谔方程解的渐近行为

摘要

本文综述了具有幂次非线性或耗散形式的非线性4阶薛定谔方程小振幅解的全局存在性和渐近行为的一些最新研究结果.考虑了散射问题的超临界非线性和临界非线性情况.%We survey our recent results on global existence and asymptotic behavior in time of small amplitude solutions to fourth-order Schr(o)dinger equations with power nonlinearities or nonlinearities of divergence form.Not only the super critical nonlinearities but also the critical ones from the view point of scattering problem are considered.