The Property of the Solution about Cauchy Problem for Fourth-Order Schrödinger Equation with Critical Time-Oscillating Nonlinearity

Abstract EN

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 + Δ 2 u + θ ( ω t ) | u | 8 / ( n - 4 ) u = 0 , where ω , t ∈ R , x ∈ R n , and θ is a periodic function.

We obtain the asymptotic property of the solution for the above equation as ω → ∞ under some conditions.