一类非自治发展方程的一致吸引子

本文研究一类非自治发展方程的渐近行为,运用算子分解及分析技巧得到了系统解的渐近正则性,由此证明一致吸引子的存在性、正则性及其结构.其中非线性项满足临界指数增长,时间依赖的外力项仅假设是平移有界而不是平移紧的.     

非线性发展方程的小模板简化Padé格式

在有理逼近的紧致格式的理论基础上,采用特别的统一的Pad啨逼近形式,构造了针对高阶非线性发展方程的、简单小模板的差商格式·　不仅保持了格式的四阶精度,而且还可以采用追赶法求解得到的3对角矩阵,或者采用三阶Runge_Kutta法直接求解积分·　计算效果通过多种算例表明是十分令人满意的·　相对于其他差分格式,此方法具有模板较小而精度保持四阶的优点·     

一类非自治发展方程一致吸引子的存在性

本文主要讨论一类非线性发展方程整体强解的长时间行为,利用文献[3]的方法,我们获得了整体强解对应的解过程族的一致耗散性,然后,通过验证一致(关于σ∈Σ)ω-极限紧,得到了系统的一致吸引子的存在性,其中非线性项满足临界指数增长条件.     

A Characteristic Equation for Non-autonomous Partial Functional Differential Equations

We characterize the exponential dichotomy of non-autonomous partial functional differential equations by means of a spectral condition extending known characteristic equations for the autonomous or time-periodic case. From this we deduce robustness results. We further study the almost periodicity of solutions to the inhomogeneous equation. Our approach is based on the spectral theory of evolution semigroups.     

Sufficient Conditions for the Oscillation of Non-autonomous Difference Equations

Abstract In this paper, we obtain sufficient conditions for the oscillation of the non-autonomous differenceequations x(n 1)-x(n) sum from i=1 to m p_i(n)x(n-r_i(n))=0,which are the discrete analog of the delay differential equations considered in[1].     

Random Partitions by Semigroup Methods

P of all partitions of {1,2,3,...}, or rather its distribution. There is a natural compact metrizable topology on P taking care of measurability questions. With respect to the maximum operation P becomes an abelian semigroup, and our first theorem characterizes random partitions as normalized positive definite functions on the subsemigroup of partitions "with finite support". We then present a new proof of Kingman's theorem stating that the exchangeable random partitions form a simplex whose extreme points are the so-called "paint-box distributions". An interesting moment problem which is still open arises in this connection.     

Fourth Order Conservative Exponential Methods for Linear Evolution Equations

A few numerical methods for linear evolution equations are developed and analyzed in this paper. These fourth order exponential methods reproduce the exact solutions for equations with time-independent evolution operators. For highly oscillatory problems with evolution operators that vary slowly in time, these methods are often more efficient than the traditional methods, since large step sizes can be used. The methods developed in this paper are also conservative for equations such as the Schrödinger equation, where the evolution operator is skew-selfadjoint.     

A Mathod to Solve Systems of Fuzzy Linear Equations

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅｗｉｌｌｃｏｎｃｅｒｎｗｉｔｈｓｏｌｖｉｎｇｔｈｅｓｙｓｔｅｍｓｏｆｆｕｚｚｙｌｉｎｅａｒｅｑｕａｔｉｏｎｓＡｘ＝ｂｆｏｒｘ，ｗｈｅｒｅＡｉｓａｍａｔｒｉｘｏｆｆｕｚｚｙｎｕｍｂｅｒｓ；ｘａｎｄｂａｒｅｖｅｃｔｏｒｓｏｆｆｕｚｚｙｎｕｍｂｅｒｓ．Ｉｎ［２］，ｕｓｉｎｇｔｈｅｎｅｗｓｏｌｕｔｉｏｎｃｏｎｃｅｐｔ，ｓｉｘｎｅｗｓｏｌｕｔｉｏｎｓａｒｅｄｅｆｉｎｅｄ．Ｔｈｉｓｄｉｓｃｕｓｓｉｏｎｗａｓｒｅｓｔｒｉｃｔｅｄｔｏｓｑ…     

Existence of Positive Solutions for N-term Non-autonomous Fractional Differential Equations

Existence of positive solutions for the nonlinear fractional differential equation D ^αu = f(x,u), 0 < α < 1 has been given (S. Zhang. J. Math. Anal. Appl. 252 (2000), 804–812) where D ^α denotes Riemann–Liouville fractional derivative. In the present work we extend this analysis for n-term non autonomous fractional differential equations. We investigate existence of positive solutions for the following initial value problem

Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time

In this paper we study maximal L ^p -regularity for evolution equations with time-dependent operators A. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the L ^p -boundedness of a class of vector-valued singular integrals which does not rely on Hörmander conditions in the time variable. This is then used to develop an abstract operator-theoretic approach to maximal regularity. The results are applied to the case of m-th order elliptic operators A with time and space-dependent coefficients. Here the highest order coefficients are assumed to be measurable in time and continuous in the space variables. This results in an L ^p (L ^q )-theory for such equations for \(p,q\in (1, \infty )\). In the final section we extend a well-posedness result for quasilinear equations to the time-dependent setting. Here we give an example of a nonlinear parabolic PDE to which the result can be applied.     

A Numerical Method to Solve Higher-Order Fractional Differential Equations

Mediterranean Journal of Mathematics - In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present...     

A Semigroup Approach to Stochastic Delay Equations in Spaces of Continuous Functions

We present a semigroup approach to stochastic delay equations of the form

一道常微分方程例题的多种解法

针对同济大学应用数学系所编《微积分》教材中一道求一阶常微分方程特解的例题,在原有幂级数解法之外,给出另三种解法,即Lyapunov人工小参数法,Adomain分解法和δ展开法.     

Semibounded Nonlinear Evolution Equations with Application to the KdV Equations

Existence of solutions for semibounded nonlinear evolution equations is established. This gives more accurate estimate of solutions and conditions of existence axe more easily validated. Our results are successfully applied to prove existence and uniqueness of solutions for some KdV type equations.     

变分方法求解脉冲微分方程

本文研究一类具有周期边值条件的脉冲微分方程解的存在性问题.通过运用临界点理论以及变分方法证明此系统存在周期解.