2009
DOI: 10.1007/s12190-009-0246-5
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On a class of nonlinear inhomogeneous Schrödinger equation

Abstract: In this paper, we study the inhomogeneous Schrödinger equationBy 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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Cited by 39 publications
(25 citation statements)
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“…However, in both papers, the authors assume that k(x) is bounded which is not verified in our case. Another type of the inhomogeneous nonlinear Schrödinger equation (INLS), but with nonlinearity of the form |x| b |u| 2σ u with b > 0, was studied by Chen and Guo [4] and Chen [3]. In these papers the authors obtain certain conditions for global existence and blow-up in the set of radial symmetric functions in H 1 (R N ).…”
Section: Introductionmentioning
confidence: 99%
“…However, in both papers, the authors assume that k(x) is bounded which is not verified in our case. Another type of the inhomogeneous nonlinear Schrödinger equation (INLS), but with nonlinearity of the form |x| b |u| 2σ u with b > 0, was studied by Chen and Guo [4] and Chen [3]. In these papers the authors obtain certain conditions for global existence and blow-up in the set of radial symmetric functions in H 1 (R N ).…”
Section: Introductionmentioning
confidence: 99%
“…For the nonlinearity with unbounded potential jxj b , Chen and Guo [3] established the local well-posedness of the Cauchy problem (1.1), (1.2) in H 1 r ¼ H 1 r ðR N Þ, where H 1 r ðR N Þ is the set of radial symmetric functions in H 1 ðR N Þ. Chen and Guo [3], Chen [4] studied the existence of blow-up solutions. Due to the unbounded potential jxj b , to our knowledge, there are few results about blow-up solutions for Cauchy problem (1.1), (1.2), which motivates us to do further research on the dynamics of blowup solutions for the Cauchy problem (1.1), (1.2 …”
Section: ð1:3þmentioning
confidence: 99%
“…The minimal energy solution RðxÞ of (1.6) is called the ground state solution (see [2,4]), and the general solution of (1.6) is called the bound state solution. Sintzoff and Willem [15] proved the existence of bound state solutions of (1.6).…”
Section: ð1:5þmentioning
confidence: 99%
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