Nonlinear Schrdinger Equation With Combined Power-Type Nonlinearities and Harmonic Potential

XU Run-zhang; XU Chuang

doi:10.3879/j.issn.1000-0887.2010.04.011

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XU Run-zhang, XU Chuang. Nonlinear Schrdinger Equation With Combined Power-Type Nonlinearities and Harmonic Potential[J]. Applied Mathematics and Mechanics, 2010, 31(4): 491-498. doi: 10.3879/j.issn.1000-0887.2010.04.011

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Nonlinear Schrdinger Equation With Combined Power-Type Nonlinearities and Harmonic Potential

doi: 10.3879/j.issn.1000-0887.2010.04.011

XU Run-zhang¹,
XU Chuang²

1.
College of Science, Harbin Engineering University, Harbin 150001, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-03-12
Publish Date: 2010-04-15

Abstract

Abstract

A class of nonlinear Schr^Ldinger equations with combined power-type nonlinearities and harmonic potential are discussed.By constructing a variational problem the potential well method is applied.The structure of the potential well and the properties of depth function are given.The invariance of some sets for the problem is shown.It is proven that if the initial data are in the potential well or out of it,the solutions will lie either in the potential well or out of it respectively.By convexity method,the sharp condition of the global well-posedness is given.
- sharp criterion,
- invariant manifold,
- harmonic potential,
- combined power-type nonlinearities

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References(30)

References

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