On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient

Chen, Jianqing

doi:10.1007/s10587-010-0046-y

Cited by 21 publications

(16 citation statements)

References 26 publications

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“…In the classical Laplacian case α = 1, if γ > 0 the problem (1.1) was treated in [7], where well-posedness was discussed via potential-well method, a recent work [27] considers a similar problem with mixed power nonlinearity. If γ < 0, the stability issues for ground states were investigated by many authors [35,14,34,17].…”

Section: (T) = M (U(t)) :=mentioning

confidence: 99%

Remarks on the inhomogeneous fractional nonlinear Schrödinger equation

Saanouni

2016

Journal of Mathematical Physics

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Abstract. Using a sharp Gagliardo-Nirenberg type inequality, well-posedness issues of the initial value problem for a fractional inhomogeneous Schrödinger equation are investigated. Consider the initial value problem for an inhomogeneous nonlinear Schrödinger equation Contentswhich models various physical contexts in the description of nonlinear waves such as propagation of a laser beam and plasma waves. For example, when γ = 0, it arises in nonlinear optics, plasma physics and fluid mechanics [2,3]. When γ > 0, it can be thought of as Date: February 16, 2016. 1991 Mathematics Subject Classification. 35Q55.

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Section: (T) = M (U(t)) :=mentioning

confidence: 99%

Remarks on the inhomogeneous fractional nonlinear Schrödinger equation

Saanouni

2016

Journal of Mathematical Physics

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“…1) It has been shown in [7] that the inequality (1.1) not only has independent interests, but also has been used to study the existence of local and global solutions of the following inhomogeneous nonlinear Schrödinger equation with harmonic potential term |x| 2 ϕ, (INLS equation henceforth) 2) is a model to describe the Bose-Einstein condensate with attractive inter-particle interactions under magnetic trap [1,18,19]. When (1.2) does not contain |x| 2 ϕ, i.e.,…”

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confidence: 96%

Sharp constant of an improved Gagliardo–Nirenberg inequality and its application

Chen

Guo

2010

Annali di Matematica

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This paper contains three parts. In the first part, we determine the best constant of an improved inequality of Gagliardo-Nirenberg interpolation (Chen, in Czechoslov Math J, in press). In the second part, we use this best constant to establish a sharp criterion for the global existence and blow-up of solutions of the inhomogeneous nonlinear Schrödinger equation with harmonic potentialin the critical nonlinearity p = 1 + (4 + 2b)/N . In the third part, we use this best constant to construct an unbounded subset S of and prove that the solutions exist globally in time for ϕ 0 ∈ S and p > 1 + (4 + 2b)/N .

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“…Proof The first equality of C(N, p, b) has been proved in [7]. We only prove the second equality of C (N, p, b).…”

Section: Preliminariesmentioning

confidence: 92%

“…The main result is contained in Theorem 5.3. In order to get these results, we use the ideas originated in [1,3,17], but we emphasize that throughout this paper, the uses of the improved Gagliardo-Nirenberg inequality and the relate best constant [7,8] are essential.…”

Section: Introductionmentioning

confidence: 99%