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61.
具有非局部边界条件的奇摄动反应扩散问题 总被引:2,自引:0,他引:2
本文研究了一类具有非局部边界条件的奇摄动反应扩散初始边值问题.在适当的条件下,利用比较定理讨论了问题解的渐近性态. 相似文献
62.
V. A. Morozov E. M. Mukhamadiev A. B. Nazimov 《Computational Mathematics and Mathematical Physics》2007,47(12):1885-1892
Regularization of singular systems of linear algebraic equations by shifts is examined. New equivalent conditions for the shift regularizability of such systems are derived. 相似文献
63.
A. V. Kravtsov 《Computational Mathematics and Mathematical Physics》2007,47(11):1875-1884
A linear problem of parametric oscillations of a low-viscous two-layer fluid in a closed vessel partially filled with a porous medium is studied. An asymptotic solution is constructed on the basis of combined application of boundary functions and averaging methods. Approximate formulas for boundaries of instability domains in the case of subharmonic and harmonic resonances are derived. 相似文献
64.
Wing-Sum Cheung Patricia J.Y. Wong 《Journal of Mathematical Analysis and Applications》2007,329(2):851-869
We consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using Schauder fixed point theorem, we establish criteria such that the system of boundary value problems has at least one fixed-sign solution. 相似文献
65.
《中国科学A辑(英文版)》2007,(7)
The double loop network(DLN)is a circulant digraph with n nodes and outdegree 2.It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems.Given the number n of nodes,how to construct a DLN which has minimum diameter?This problem has attracted great attention.A related and longtime unsolved problem is:for any given non-negative integer k,is there an infinite family of k-tight optimal DLN?In this paper,two main results are obtained:(1)for any k≥0,the infinite families of k-tight optimal DLN can be constructed,where the number n(k,e,c)of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c.(2)for any k≥0, an infinite family of singular k-tight optimal DLN can be constructed. 相似文献
66.
Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes. 相似文献
67.
In this paper, we prove Lp-boundedness of hyperbolic singular integral operators for kernels satisfying weakened regularity conditions, where 1
相似文献
68.
In general, we will use the numerical differentiation when dealing with the differential equations. Thus the differential equations can be transformed into algebraic equations and then we can get the numerical solutions. But as we all have known, the numerical differentiation process is very sensitive to even a small level of errors. In contrast it is expected that on average the numerical integration process is much less sensitive to errors. In this paper, based on the Sinc method we provide a new method using Sinc method incorporated with the double exponential transformation based on the interpolation of the highest derivatives (SIHD) for the differential equations. The error in the approximation of the solution is shown to converge at an exponential rate. The numerical results show that compared with the exiting results, our method is of high accuracy, of good convergence with little computational efforts. It is easy to treat nonhomogeneous mixed boundary condition for our method, which is unlike the traditional Sinc method. 相似文献
69.
Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System 总被引:1,自引:1,他引:0
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This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed system. Based on Poincare map, a series of blow-up transformations and the theory of integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied. 相似文献
70.
The generalized Morrey spaces are introduced under the hypothesis that Rn is endowed with the general parabolic metric , and the boundedness properties are established in generalized Morrey spaces for a class of singular integral operators, which include Calderon-Zygmund singular integrals and their commutators with BMO. 相似文献