On a class of quasilinear Schrdinger equations 被引量：1

On a class of quasilinear Schrdinger equations

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摘要 A type of quasilinear Schrodinger equations in two space dimensions which describe attractive Bose-Einstein condensates in physics is discussed. By establishing the property of the equation and applying the energy method, the blowup of solutions to the equation are proved under certain conditions. At the same time, by the variational method, a sutficient condition of global existence which is related to the ground state of a classical elliptic equation is obtained. A type of quasilinear Schrodinger equations in two space dimensions which describe attractive Bose-Einstein condensates in physics is discussed. By establishing the property of the equation and applying the energy method, the blowup of solutions to the equation are proved under certain conditions. At the same time, by the variational method, a sutficient condition of global existence which is related to the ground state of a classical elliptic equation is obtained.

作者舒级张健

机构地区 Key Laboratory of Computer Software College of Mathematics and Software Science

出处《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第7期981-986,共6页 应用数学和力学（英文版）

基金 Project supported by the Scientific Research Foundation of Sichuan Provincial Commission of Education(No.SZD0406) the Scientific Research Fund of Sichuan Normal University

关键词 quasilinear Schrodinger equations BLOWUP global existence ground state Bose-Einstein condensates quasilinear Schrodinger equations, blowup, global existence, ground state Bose-Einstein condensates

分类号 O175.2 [理学—基础数学]

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1Markus Poppenberg,Klaus Schmitt,Zhi-Qiang Wang.On the existence of soliton solutions to quasilinear Schr?dinger equations[J].Calculus of Variations and Partial Differential Equations.2002(3)
2Jian Zhang.Stability of Attractive Bose–Einstein Condensates[J].Journal of Statistical Physics (-).2000(3-4)
3Anne de Bouard,Nakao Hayashi,Jean-Claude Saut.Global Existence of Small Solutions to a Relativistic Nonlinear Schr?dinger Equation[J].Communications in Mathematical Physics.1997(1)
4Man Kam Kwong.Uniqueness of positive solutions of Δu?u+up=0 in Rn[J].Archive for Rational Mechanics and Analysis.1989(3)
5Michael I. Weinstein.Nonlinear Schr?dinger equations and sharp interpolation estimates[J].Communications in Mathematical Physics.1983(4)
6Rainer W. Hasse.A general method for the solution of nonlinear soliton and kink Schr?dinger equations[J].Zeitschrift für Physik B Condensed Matter and Quanta.1980(1)
7Cazenave T.An introduction to nonlinear Schr(?)dinger equations[]..1989
8Kwong M K.Uniqueness of positive solutions ofΔu-u+u~p=0 in R~N[].Archive for Rational Mechanics and Analysis.1989
9Glassey R T.On the blowup of nonlinear Schr(?)dinger equations[].Journal of Mathematical Physics.1977
10Zhang Jian.The blowup properties of the initial-boundary problem for second order derivative nonlinear Schr(?)dinger equations[].Acta Mathematica.1994