共查询到12条相似文献,搜索用时 6 毫秒
1.
《偏微分方程通讯》2013,38(3-4):693-704
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《偏微分方程通讯》2013,38(11-12):2311-2331
ABSTRACT We study here an asymptotic limit of the Schrödinger–Poisson system. We prove that the current converges toward a dissipative solution of the Euler equations when we consider a semi-classical quasi-neutral limit. The proof involves the modulated energy introduced by Brenier in Ref. [2]. 相似文献
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We give a lower bound for the first gap λ_2—λ_1 of the twolowerst eigenvalues of the Schr(o|¨)dinger operator-△+W(p) with the Dirichletboundary condition and a strictly convex potential W(p)on M in which M is acompact simple Riemannian manifold with smooth strictly convex boundary (?)MHere a compact Riemannian manifold M is said to be simple if M~(?)M istopologically R~2.We prove thatλ_2-λ_1≥(π~2)/(d~2)+min{0,-(n-1)K}where d is the diameter of M and-(n-1)K,(K≥0)the lower bound of theRicci curvature of M.This work generalizes the results in the classical Eucli-dean situation due to Singer,Wong and Yau,Yu and Zhong to a kind of curvedRiemannian manifold. 相似文献
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陈韵梅 《应用数学学报(英文版)》1985,2(3):191-212
In this paper,we discuss the problem for the nonlinear Schr(?)dinger equation(?)where Ω is the exterior domain of a compact set in B~n,a_j(u)=O(|u|),b_j(u)=O(|u|)(1≤j≤n),c(u)=O(|u|~2)near u=0.If n≥5,some Sobolev norm of u_0(x)is sufficiently small,under suitableassumptions on smoothnessand and compatibility and the shape of Ω,we get that the problem has aunique global solution u(t,x),with the decay estimate‖u(t,·)‖_(L(?)(Ω))=O(t~(-n/4)),‖u(t,·)‖_(L~4(Ω))=O(t~(-n/4)),t→+∞. 相似文献
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We consider the blow-up solutions to the following coupled nonlinear Schrodinger equations■.On the basis of the conservation of mass and energy,we establish two sufficient conditions to obtain the existence of a blow-up for radially symmetric solutions.These results improve the blow-up result of Li and Wu [10] by dropping the hypothesis of finite variance((|x|u0,|x|v0) ∈L2(RN) × L2(RN)). 相似文献
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The existence and multiplicity of positive solutions for equation(1.1) with the new critical exponent 4
* shall be investigated in a high dimension.The conclusions extend the relative results recently attained in [1] for the one-dimensional case.More precisely,as the coefficient a(x) in the nonlinearity is sign-changing,the modified term 2(Δ(|u|2))u is still helpful for obtaining multiple positive solutions in a high dimension,even if a sign condition like■(als... 相似文献
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The purpose of this paper is to present a comparison between the modified nonlinear Schro¨dinger (MNLS) equation and the focusing and defocusing variants of the (unmodified) nonlinear Schr¨odinger (NLS) equation in the semiclassical limit. We describe aspects of the limiting dynamics and discuss how the nature of the dynamics is evident theoretically through inverse-scattering and noncommutative steepest descent methods. The main message is that, depending on initial data, the MNLS equation can behave either like the defocusing NLS equation, like the focusing NLS equation (in both cases the analogy is asymptotically accurate in the semiclassical limit when the NLS equation is posed with appropriately modified initial data), or like an interesting mixture of the two. In the latter case, we identify a feature of the dynamics analogous to a sonic line in gas dynamics, a free boundary separating subsonic flow from supersonic flow. 相似文献
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《高校应用数学学报(英文版)》1999,(1)
§1IntroductionMuchatentionhasbeendevotedtothenonlinearSchrodingerequations[1~3].Thisbe-causemanyphysicalphenomenacanbedescrib... 相似文献
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In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrdinger-Kirchhoff type -εpMεp_N∫RN|▽u|p△pu+V(x)|u|p-2u=f(u) in R~N, where △_p is the p-Laplacian operator, 1 p N, M :R~+→R~+ and V :R~N→R~+are continuous functions,ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and LyusternikSchnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation. 相似文献
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郭柏灵 《数学物理学报(B辑英文版)》1989,(1)
The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term. 相似文献
12.
G. Crombez 《分析论及其应用》1997,(4)
We present a parallel iterative algorithm to find the shortest distance projection of a given point onto the intersection of a finite number of closed convex sets in a real Hilbert space ; the number of sets used at each iteration stept corresponding to the number of available processors, may be smaller than the total number of sets. The relaxation coefficient at each iteration step is determined by a geometrical condition in an associated Hilbert space, while for the weights mild conditions are given to assure norm convergence of the resulting sequence. These mild conditions leave enough flexibility to determine the weights more specifically in order to improve the speed of convergence. 相似文献