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Phenomena of Blowup and Global Existence of the Solution to a Nonlinear Schrödinger Equation

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  • Xiaowei An
  • Desheng Li
  • Xianfa Song

Abstract

We consider the following Cauchy problem: −iut = Δu − V(x)u + f(x, |u|2)u + (W(x)⋆|u|2)u, x ∈ ℝN, t > 0, u(x, 0) = u0(x), x ∈ ℝN, where V(x) and W(x) are real‐valued potentials and V(x) ≥ 0 and W(x) is even, f(x, |u|2) is measurable in x and continuous in |u|2, and u0(x) is a complex‐valued function of x. We obtain some sufficient conditions and establish two sharp thresholds for the blowup and global existence of the solution to the problem.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:238410
DOI: 10.1155/2013/238410
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