Remarks on Scattering Properties of the Solution to a Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities

Details Remarks on Scattering Properties of the Solution to a Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities Remarks on Scattering Properties of the Solution to a Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities

2010-09-02

arxiv.org/abs/1009.0325v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

In this paper, we consider the Cauchy problem of Nonlinear Schr\"{o}dinger equation \begin{align*} \left\{\begin{array}{ll}&i u_t+\Delta u=\lambda_1|u|^{p_1}u+\lambda_2|u|^{p_2}u, \quad t\in\mathbb{R}, \quad x\in\mathbb{R}^N &u(0,x)=\varphi(x), \quad x\in\mathbb{R}^N, \end{array} \right. \end{align*} where $N\geq 3$, $0

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