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On a class of nonlinear inhomogeneous Schrödinger equation

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Abstract

In this paper, we study the inhomogeneous Schrödinger equation

$$i\varphi_{t}=-\triangle\varphi -|x|^{b}|\varphi|^{p-1}\varphi,\quad x\in \mathbb{R}^{N}.$$

By using variational methods and a refined interpolation inequality, we establish some simple but sharp conditions on the solutions which exist globally or blow up in a finite time. An interesting result is that we obtain the existence of global solution for arbitrarily large data.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, P.R. China

    Jianqing Chen

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  1. Jianqing Chen
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Correspondence to Jianqing Chen.

Additional information

Supported by Youth Foundation of NSFC (10501006) and by the program for NCETFJ.

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Chen, J. On a class of nonlinear inhomogeneous Schrödinger equation. J. Appl. Math. Comput. 32, 237–253 (2010). https://doi.org/10.1007/s12190-009-0246-5

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  • DOI: https://doi.org/10.1007/s12190-009-0246-5

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