Article ID Journal Published Year Pages File Type
4622066 Journal of Mathematical Analysis and Applications 2008 12 Pages PDF
Abstract

This paper discusses a class of inhomogeneous nonlinear Schrödinger equation{i∂tu(t,x)=−Δu(t,x)−V(x)|u(t,x)|p−1u(t,x),u(0,x)=u0(x), where (t,x)∈R×R2(t,x)∈R×R2, V(x)V(x) satisfies some assumptions.By a constrained variational problem, we firstly define some cross-constrained invariant sets for the inhomogeneous nonlinear Schrödinger equation, then we obtain some sharp conditions for global existence and blow up of solutions. As a consequence it is shown that the solution is globally well-posed in Hr1(R2) with the H1H1-norm of the initial data u0u0 which is dominated by the minimal value of the constrained variational problem.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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