共查询到20条相似文献,搜索用时 15 毫秒
1.
** Email: chenguanggan{at}hotmail.com This paper is concerned with the non-linear GrossPitaevskiiequation which describes the attractive BoseEinsteincondensate under a magnetic trap. By an intricate variationalargument we derive out a sharp threshold of blowing up and globalexistence by applying the potential well argument and the concavitymethod. Furthermore, we answer the question: How small are theinitial data, the global solutions of the Cauchy problem ofthe equation exist for [graphic: see PDF] 相似文献
2.
Shu-Yu Hsu 《Mathematische Annalen》2006,334(1):153-197
Let a1,a2, . . . ,am ∈ ℝ2, 2≤f ∈ C([0,∞)), gi ∈ C([0,∞)) be such that 0≤gi(t)≤2 on [0,∞) ∀i=1, . . . ,m. For any p>1, we prove the existence and uniqueness of solutions of the equation ut=Δ(logu), u>0, in satisfying and logu(x,t)/log|x|→−f(t) as |x|→∞, logu(x,t)/log|x−ai|→−gi(t) as |x−ai|→0, uniformly on every compact subset of (0,T) for any i=1, . . . ,m under a mild assumption on u0 where We also obtain similar existence and uniqueness of solutions of the above equation in bounded smooth convex domains of ℝ2 with prescribed singularities at a finite number of points in the domain. 相似文献
3.
Xiaoping Yuan 《中国科学A辑(英文版)》1998,41(6):595-605
The boundedness of all solutions is shown for Duffing-type equations
wherep
1,p
2,...,p
2n are of period 1 and of Lipschitzian continuity andp
n+1,...,p
2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing-type equations does
not require the smoothness in the time-variable, thus answering the question posed by Dieckerhoff and Zehnder. 相似文献
4.
An existence theorem of positive solutions for elastic beam equation with both fixed end-points 总被引:4,自引:0,他引:4
JiangXiufen YaoQingliu 《高校应用数学学报(英文版)》2001,16(3):237-240
Abstract. By using the degree theory on cone an existence theorem of positive solution for aclass of fourth-order two-point BVP‘s is obtained. This class of BVP‘s usually describes the de-formation of the elastic beam with both fixed end-points. 相似文献
5.
Yong-ping Sun 《高校应用数学学报(英文版)》2011,26(3):253-264
This paper investigates the boundary value problem for elastic beam equation of the form
u"(t) = q(t)f(t,u(t)u¢(t),u"(t),u"¢(t)),0 < t < 1,u'(t) = q(t)f(t,u(t)u'(t),u'(t),u'(t)),0 < t < 1, 相似文献
6.
We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut- ΔN∞u = f,where ΔN∞denotes the so-called normalized infinity Laplacian given by ΔN∞u =1|Du|2 D2 uD u, Du. 相似文献
7.
斯仁道尔吉 《高校应用数学学报(英文版)》2001,16(1):19-24
Abstract. Some exact travelling wave solutions and rational travelling wave solutions of a sur-face wave equation in a convecting fluid are given in this paper. 相似文献
8.
Barcenas Diomedes; Leiva Hugo; Urbina Wilfredo 《IMA Journal of Mathematical Control and Information》2006,23(1):1-9
** Email: Leiva{at}ula.ve In this paper we study the controllability of the followingcontrolled OrnsteinUhlenbeck equation [graphic: see PDF] then the system is approximately controllable on [0, t1]. Moreover,the system can never be exactly controllable. 相似文献
9.
一般变系数KdV方程的精确解 总被引:7,自引:0,他引:7
LiuXiqiang JiangSong 《高校应用数学学报(英文版)》2001,16(4):377-380
By asing the nonclassical method of symmetry reductions, the exact solutions for general variable-coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don‘t exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable-coefficient KdV equation is given. 相似文献
10.
刘玉玲 《纯粹数学与应用数学》2007,23(3):414-419
通过利用 Krasnosel'skii 不动点定理的扩充定理,对于一类含导数的一维p-Laplacian 方程 m-点边值问题建立了至少一个正解的存在性定理,并给出例子加以说明. 相似文献
11.
Global existence and blow-up for the solutions to nonlinear parabolic-elliptic system modelling chemotaxis 总被引:1,自引:0,他引:1
In this paper we study the global in-time and blow-up solutionsfor the simplified KellerSegel system modelling chemotaxis.We prove that there is a critical number which determines theoccurrence of blowup in the two-dimensional case for 1 <p < 2. In three- or higher-dimensional cases, we show thatthe radial symmetrical solution will blow up if 1 < p <N/N2 (N 3) for non-negative initial value. 相似文献
12.
考虑一类高阶分数阶差分方程边值问题.构造相关的格林函数,利用不等式技巧,分析格林函数的特征性质.运用不动点指数理论,获得了该分数阶差分方程边值问题存在多重正解的充分条件,举例说明了所获理论的有效性. 相似文献
13.
In this paper, we consider the complex Swift-Hohenberg(CSH) equation $\frac{\partial u}{\partial t}=\lambda u-(\alpha+\mathrm{i}\beta)\l(1+\frac{\partial^2}{\partial x^2}\r)^2u-(\sigma+\mathrm{i}\rho)|u|^2u $ subject to periodic boundary conditions. Using an infinite dimensional KAM theorem, we prove that there exist a continuous branch of periodic solutions and a Cantorian branch of quasi-periodic solutions for
the above equation. 相似文献
14.
Jacob Fox 《Discrete Mathematics》2008,308(20):4773-4778
We prove that for every 4-coloring of {1,2,…,n}, with each color class having cardinality more than (n+1)/6, there exists a solution of the equation x+y=z+w with x, y, z and w belonging to different color classes. The lower bound on a color class cardinality is tight. 相似文献
15.
Ahmed Salem 《Journal of Applied Analysis & Computation》2020,10(6):2557-2574
Recently, Khalili and Yadollahzadeh [ Y. Khalili and M. Yadollahzadeh, Existence results for a new class of nonlinear Langevin equations of fractional orders, Iranian J. Sci. Tech., Trans. A: Sci., 2019, 43(5), 2335–2342] have investigated the uniqueness and existence of solution $u(t),~t\in[0,1]$ for a class of nonlocal boundary conditions to fractional Langevin equation. The authors used the boundary condition $u"(0)=0$ by incorrect method. In the current contribution, we show the correct method for using this condition and study the existence and uniqueness of solution for the same class of equation in slightly different form with anti-periodic and nonlocal integral boundary conditions as well as the boundary condition $u"(0)=0$. An exemplar is provided to illustrate our results. 相似文献
16.
17.
Group-invariant solutions, non-group-invariant solutions and conservation laws of Qiao equation 下载免费PDF全文
This paper considers a completely integrable nonlinear wave equation which is called Qiao equation. The equation is reduced via Lie symmetry analysis. Two classes of new exact group-invariant solutions are obtained by solving the reduced equations. Specially, a novel technique is proposed for constructing group-invariant solutions and non-group-invariant solutions based on travelling wave solutions. The obtained exact solutions include a set of traveling wave-like solutions with variable amplitude, variable velocity or both. Nonlocal conservation laws of Qiao equation are also obtained with the corresponding infinitesimal generators. 相似文献
18.
A vector functional-difference equation of the first order witha special matrix coefficient is analysed. It is shown how itcan be converted into a RiemannHilbert boundary-valueproblem on a union of two segments on a hyper-elliptic surface.The genus of the surface is defined by the number of zeros andpoles of odd order of a characteristic function in a strip.An even solution of a symmetric RiemannHilbert problemis also constructed. This is a key step in the procedure fordiffraction problems. The proposed technique is applied forsolving in closed form a new model problem of electromagneticscattering of a plane wave obliquely incident on an anisotropicimpedance half-plane (all the four impedances are assumed tobe arbitrary). 相似文献
19.
In this paper,we consider the global existence of solutions for the Cauchy problem of the generalized sixth order bad Boussinesq equation.Moreover,we show that the supremum norm of the solution decays algebraically to zero as(1+t)(1/7)when t approaches to infnity,provided the initial data are sufciently small and regular. 相似文献
20.
Weiqin Yu Na Li Fangqi Chen Shouwei Zhao 《Journal of Applied Analysis & Computation》2016,6(4):968-980
Utilizing the methods of dynamical system theory, the Dullin-Gottwald-Holm equation is studied in this paper. The dynamical behaviors of the traveling wave solutions and their bifurcations are presented in different parameter regions. Furthermore, the exact explicit forms of all possible bounded solutions, such as solitary wave solutions, periodic wave solutions and breaking loop wave solutions are obtained. 相似文献
|