The property of the solution about Cauchy problem for fourth-order Schrödinger equation with critical time-oscillating nonlinearity (Q1722282)

Summary: We study the property of the solution in Sobolev spaces for the Cauchy problem of the following fourth-order Schrödinger equation with critical time-oscillating nonlinearity \(i u_t + \Delta^2 u + \theta(\omega t) | u |^{8 /(n - 4)} u = 0\), where \(\omega, t \in R\), \(x \in R^n\), and \(\theta\) is a periodic function. We obtain the asymptotic property of the solution for the above equation as \(\left|\omega\right| \rightarrow \infty\) under some conditions.