共查询到20条相似文献,搜索用时 281 毫秒
1.
Jaime Angulo Pava 《Journal of Differential Equations》2007,235(1):1-30
This work is concerned with stability properties of periodic traveling waves solutions of the focusing Schrödinger equation
iut+uxx+2|u|u=0 相似文献
2.
In this paper, one-dimensional (1D) nonlinear Schrödinger equation
iut−uxx+mu+4|u|u=0 相似文献
3.
Ioan Bejenaru 《Journal of Functional Analysis》2006,233(1):228-259
We establish that the quadratic non-linear Schrödinger equation
iut+uxx=u2, 相似文献
4.
João Marcos do Ó Everaldo Medeiros 《Journal of Mathematical Analysis and Applications》2008,345(1):286-304
In this paper we study a class of nonhomogeneous Schrödinger equations
−Δu+V(x)u=f(u)+h(x) 相似文献
5.
This paper is concerned with the standing wave for a class of nonlinear Schrödinger equations
iφt+Δφ−2|x|φ+μ|φ|p−1φ+γ|φ|q−1φ=0, 相似文献
6.
Teng Fei Zhao 《数学学报(英文版)》2017,33(7):911-925
We consider the defocusing nonlinear Schr?dinger equations iu_t +△u =|u|~(p_u) with p being an even integer in dimensions d≥ 5. We prove that an a priori bound of critical norm implies global well-posedness and scattering for the solution. 相似文献
7.
In this article we prove the property of unique continuation (also known for C∞ functions as quasianalyticity) for solutions of the differential inequality |Δu|?|Vu| for V from a wide class of potentials (including class) and u in a space of solutions YV containing all eigenfunctions of the corresponding self-adjoint Schrödinger operator. Motivating question: is it true that for potentials V, for which self-adjoint Schrödinger operator is well defined, the property of unique continuation holds? 相似文献
8.
Let u be the weak solution to the degenerate Schrödinger equation with singular coefficients in Lipschitz domain as following
−div(w(x)A(x)∇u(x))+V(x)u(x)w(x)=0, 相似文献
9.
Let us consider the time-dependent Schrödinger equation,
iφt=−Δφ+V(x,t)φ, 相似文献
10.
Claudio Bonanno Pietro d'Avenia Marco Ghimenti Marco Squassina 《Journal of Mathematical Analysis and Applications》2014
We investigate the soliton dynamics for a class of nonlinear Schrödinger equations with a non-local nonlinear term. In particular, we consider what we call generalized Choquard equation where the nonlinear term is (|x|θ−N?|u|p)|u|p−2u. This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate. 相似文献
11.
Xiangqing Zhao Cuihua Guo Wancheng Sheng 《Journal of Mathematical Analysis and Applications》2011,382(1):97-109
In this paper we study the Cauchy problem of the non-isotropically perturbed fourth-order nonlinear Schrödinger type equation: ((x1,x2,…,xn)∈Rn, t?0), where a is a real constant, 1?d<n is an integer, g(x,|u|)u is a nonlinear function which behaves like α|u|u for some constant α>0. By using Kato method, we prove that this perturbed fourth-order Schrödinger type equation is locally well-posed with initial data belonging to the non-isotropic Sobolev spaces provided that s1,s2 satisfy the conditions: s1?0, s2?0 for or for with some additional conditions. Furthermore, by using non-isotropic Sobolev inequality and energy method, we obtain some global well-posedness results for initial data belonging to non-isotropic Sobolev spaces . 相似文献
12.
Under suitable assumptions on the potentials V and a, we prove that if u∈C([0,1],H1) is a solution of the linear Schrödinger equation
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14.
In this paper, we consider one-dimensional nonlinear Schrödinger equation iut−uxx+V(x)u+f(2|u|)u=0 on [0,π]×R under the boundary conditions a1u(t,0)−b1ux(t,0)=0, a2u(t,π)+b2ux(t,π)=0, , for i=1,2. It is proved that for a prescribed and analytic positive potential V(x), the above equation admits small-amplitude quasi-periodic solutions corresponding to d-dimensional invariant tori of the associated infinite-dimensional dynamical system. 相似文献
15.
The authors of this article study the existence and uniqueness of weak solutions of the initial-boundary value problem for ut =div((|u|σ + do)|▽u|P(x,t)-2▽u) +f(x,t) (0 < σ < 2).They apply the method o... 相似文献
16.
Haifeng Shang 《Journal of Mathematical Analysis and Applications》2011,378(2):578-591
The Cauchy problem for a singular parabolic equation with gradient term of the form
ut−div(|Du|p−2Du)=|Duqσ| 相似文献
17.
Songzhe Lian Chunling Cao Hongjun Yuan 《Journal of Mathematical Analysis and Applications》2008,342(1):27-38
The authors of this paper study the Dirichlet problem of the following equation
ut−div(|u|ν(x,t)∇u)=f−|u|p(x,t)−1u. 相似文献
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19.
Jiansheng Geng 《Journal of Differential Equations》2005,209(1):1-56
In this paper, one-dimensional (1D) nonlinear Schrödinger equation
20.
Roger Peres de Moura 《Journal of Mathematical Analysis and Applications》2007,326(2):1254-1267
We establish local well-posedness for small initial data in the usual Sobolev spaces Hs(R), s?1, and global well-posedness in H1(R), for the Cauchy problem associated to the nonlocal nonlinear Schrödinger equation