共查询到20条相似文献,搜索用时 31 毫秒
1.
V. L. Vereshchagin 《Theoretical and Mathematical Physics》2006,148(3):1199-1209
We write formulas for soliton solutions of the discrete Toda chain and pose the integrable boundary value problem for this
chain. We find conditions for the parameters (discrete spectrum points, transmission coefficients, and the corresponding factors)
whereby solutions of the integrable boundary value problem are selected from all soliton solutions. As a result, we construct
two hierarchies of soliton solutions of the specified problem with even and odd soliton numbers and find an explicit form
of the conditions for the parameters.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 3, pp. 387–397, September, 2006. 相似文献
2.
Haiyan Lv 《Journal of Difference Equations and Applications》2013,19(6):987-1015
In this paper, eigenvalues of perturbed discrete linear Hamiltonian systems are considered. A new variational formula of eigenvalues is first established. Based on it, error estimates of eigenvalues of systems with small perturbation are given under certain non-singularity conditions. Small perturbations of the coefficient functions, the weight function and the coefficients of the boundary condition are all involved. As a direct consequence, continuous dependence of eigenvalues on boundary value problems is obtained under the non-singularity conditions. In addition, two examples are presented to illustrate the necessity of the non-singularity conditions and the complexity of the problem in the singularity case. 相似文献
3.
Using critical point theory and some monotonicity results we consider the existence of solutions to a boundary value problem connected with the discrete elliptic equation with a positive parameter. 相似文献
4.
Wolf-Jürgen Beyn Jens Rottmann-Matthes 《Numerical Functional Analysis & Optimization》2013,34(5-6):603-629
In many applications such as the stability analysis of traveling waves, it is important to know the spectral properties of a linear differential operator on the whole real line. We investigate the approximation of this operator and its spectrum by finite interval boundary value problems from an abstract point of view. Under suitable assumptions on the boundary operators, we prove that the approximations converge regularly (in the sense of discrete approximations) to the all line problem, which has strong implications for the behavior of resolvents and spectra. As an application, we obtain resolvent estimates for abstract coupled hyperbolic–parabolic equations. Furthermore, we show that our results apply to the FitzHugh–Nagumo system. 相似文献
5.
Milan Práger 《Applications of Mathematics》1998,43(4):311-320
A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained. 相似文献
6.
Ferhan M. Atıcı 《Journal of Difference Equations and Applications》2013,19(4):445-456
In this paper, we introduce a two-point boundary value problem for a finite fractional difference equation. We invert the problem and construct and analyse the corresponding Green's function. We then provide an application and obtain sufficient conditions for the existence of positive solutions for a two-point boundary value problem for a nonlinear finite fractional difference equation. 相似文献
7.
R. D. M. Garcia C. E. Siewert 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,57(1):94-122
An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate
solutions to the problem of sound-wave propagation in a rarefied gas. The analysis and the numerical work are based on a rigorous
form of the linearized Boltzmann equation (for rigid-sphere interactions), and in contrast to many other works formulated
(for an infinite medium) without a boundary condition, the solution reported here satisfies a boundary condition that models
a diffusely-reflecting vibrating plate. In addition and in order to investigate the effect of kinetic models, solutions are
developed for the BGK model, the S model, the Gross-Jackson model, as well as for the (newly defined) MRS model and the CES
model. While the developed numerical results are compared to available experimental data, emphasis in this work is placed
on the solutions of the problem of sound-wave propagation as described by the linearized Boltzmann equation and the five considered
kinetic models.
Received: November 22, 2004; revised: February 24, 2005 相似文献
8.
The spectrum of the elasticity problem for a spiked body 总被引:2,自引:1,他引:1
S. A. Nazarov 《Siberian Mathematical Journal》2008,49(5):874-893
We establish the existence of continuous spectrum for the operator of the linear elasticity problem in a three-dimensional domain with a sufficiently sharp spiked singularity of the boundary. We obtain some information about the structure of the spectrum and verify the weighted Korn inequality, which enables us to prove that the spectrum is discrete for insufficiently sharp spikes. We state some open questions. 相似文献
9.
A. A. Nikitin 《Differential Equations》2013,49(5):645-653
We prove the uniqueness of a generalized solution of an initial-boundary value problem for the wave equation with boundary conditions of the third and second kind. In addition, we find a closed-form expression for the analytic solution of that problem with zero initial data. The result plays an important role in the investigation of the boundary control problem. We show how to use the obtained solution for the investigation of the boundary control problem in the case of subcritical time intervals for which the solution of the boundary control problem, if it exists at all, is unique. We obtain necessary and sufficient conditions for the existence of a unique solution in a class admitting the existence of finite energy. 相似文献
10.
研究了一类二阶非线性差分方程两点边值问题非平凡解的存在性.假设该问题在无穷远点及零点处均是共振的,利用变分方法,同时考虑正、负能量泛函的临界点,在一定的假设条件下,通过临界群的计算,证明了该问题至少存在一个非平凡解. 相似文献
11.
Turhan Koprubasi Ram N. Mohapatra 《Mathematical Methods in the Applied Sciences》2023,46(2):1466-1478
In this paper, an inverse scattering problem for discrete Sturm–Liouville equation with eigenparameter-dependent boundary condition is investigated. In quest of finding scattering function and the main equation of this problem, the uniqueness of the kernel is proven. Also, an appropriate Levinson-type formula based on the continuity of scattering function is given. 相似文献
12.
C. E. Siewert 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(2):273-292
An analytical version of the discrete-ordinates method (the ADO method) is used to establish a concise and particularly accurate solution to the temperature-jump problem for a binary gas mixture described by the McCormack kinetic model. The solution yields, in addition to the temperature-jump coefficient for the general (specular–diffuse) case of Maxwell boundary conditions for each of the two species, the density and temperature profiles for both types of particles. Numerical results are reported for two binary mixtures (Ne-Ar and He-Xe) with various molar concentrations. The algorithm is considered especially easy to use, and the developed (FORTRAN) code requires typically less than a second on a 2.2 GHz Pentium 4 machine to compute all quantities of interest.Received: November 18, 2003; revised April 14, 2004 相似文献
13.
R. R. Gadyl’shin S. V. Rep’evskii E. A. Shishkina 《Proceedings of the Steklov Institute of Mathematics》2016,292(1):76-90
A boundary-value problem of finding eigenvalues is considered for the negative Laplace operator in a disk with Neumann boundary condition on almost all the circle except for a small arc of vanishing length, where the Dirichlet boundary condition is imposed. A complete asymptotic expansion with respect to a parameter (the length of the small arc) is constructed for an eigenvalue of this problem that converges to a double eigenvalue of the Neumann problem. 相似文献
14.
We consider an inverse boundary problem for a general second order self-adjoint elliptic differential operator on a compact differential manifold with boundary. The inverse problem is that of the reconstruction of the manifold and operator via all but finite number of eigenvalues and traces on the boundary of the corresponding eigenfunctions of the operator. We prove that the data determine the manifold and the operator to within the group of the generalized gauge transformations. The proof is based upon a procedure of the reconstruction of a canonical object in the orbit of the group. This object, the canonical Schrödinger operator, is uniquely determined via its incomplete boundary spectral data. 相似文献
15.
Sören Christensen Albrecht Irle 《Stochastics An International Journal of Probability and Stochastic Processes》2019,91(5):728-753
We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height variables. In case that the original problem has a one-sided solution and the auxiliary problem has a monotone structure, the corresponding myopic stopping time is optimal for the original problem as well. This elementary line of argument directly leads to a characterization of the optimal boundary in the original problem. The optimal threshold is given by the threshold of the myopic stopping time in the auxiliary problem. Supplying also a sufficient condition for our approach to work, we obtain solutions for many prominent examples in the literature, among others the problems of Novikov-Shiryaev, Shepp-Shiryaev, and the American put in option pricing under general conditions. As a further application we show that for underlying random walks (and Lévy processes in continuous time), general monotone and log-concave reward functions g lead to one-sided stopping problems. 相似文献
16.
应用锥上的不动点定理和锥理论,我们在对非线性项的不同假设下分别得到了一类2m阶离散Lidstone BVP特征值的存在区间. 相似文献
17.
基于透射边界条件的高阶离散型角点条件 总被引:2,自引:0,他引:2
对波动方程的数值模拟中,在有限区域建立吸收边界条件,其中对区域角点的处理是一个很重要的问题.随着吸收边界条件阶数的提高,与之匹配的角点条件也越难建立.MTF是一种离散型吸收边界条件.在此,对于二维问题,基于MTF建立离散型高阶角点条件,对计算区域角点处理时,在区域对角线方向上建立N阶MTF公式.问题也可推广到三维.数值结果证实了我们的猜测. 相似文献
18.
We consider linear and nonlinear boundary value problems for third-order difference equations with three-point right focal boundary conditions. In the linear case, the existence of positive solutions corresponding to the first eigenvalue of the problem is established and an interval estimate for the first eigenvalue is obtained. In the nonlinear case, sufficient conditions for the existence and nonexistence of positive solutions are obtained. An example is included at the end of the paper to illustrate the sharpness of our results. 相似文献
19.
朱玉扬 《应用数学与计算数学学报》2010,24(2):31-41
本文研究如下一种场站设置问题:设S是欧空间R~m中由有限个点A_1,A_2,…,A_n组成的集合.d(A_i,A_j)表示点A_i和A_j之间的距离.令μ(m,n)=σ(S)/(d(S))(SR~m,|S|=n),infμ(m,n)=min{=σ(S)/(d(S))|SR~m,|S|=n}.估计infμ(m,n)的值.本文通过分类处理,区域控制,求边界极值等分析方法给出infμ(2,5)=9+2(3(1/2))等结果. 相似文献
20.
Yusuke Higuchi 《Annals of Global Analysis and Geometry》2003,24(3):201-230
We introduce the boundary area growth as a new quantity for an infinite graph. Using this, we give some upper bounds for the bottom of the spectrum of the discrete Laplacian which relates closely to the transition operator. We also give some applications and examples. 相似文献