Global attractivity in a perturbed linear delay differential equation

In the main result of this paper, some sharp conditions are obtained for global attractivity in a scalar perturbed linear delay differential equation. The proof of the main theorem is based on a new estimate for the infinite integral of the absolute value of the fundamental solution of a linear delay differential equation. We also derive sufficient conditions for asymptotic stability of a system of linear delay differential equations.     

求解一类模糊线性微分系统的结构元方法

基于模糊结构元方法,研究了由对称模糊结构元线性生成的一般模糊线性微分系统和双重的一般模糊线性微分系统,给出了模糊线性微分系统解存在的充要条件,得到了结构元线性生成的齐次、非齐次以及双重一般模糊线性微分系统求解方法。最后,给出了这类系统的实际应用。     

Regular boundary value problems with a discontinuous coefficient,functional-multipoint conditions,and a linear spectral parameter

We consider a linear differential equation which includes a linear abstract operator, with a piecewise constant coefficient at the principal differential term, together with multipoint boundary-transmission conditions, including linear functionals. The spectral parameter appears linearly in the equation and may appear also linearly in the boundary-transmission conditions. We prove an isomorphism and coerciveness of the problem with respect to the spectral parameter and the space variable.     

Lyapunov-type inequality for a class of even-order differential equations

In this paper, we generalize the well-known Lyapunov-type inequality for second-order linear differential equations to a class of even-order linear differential equations, the results of this paper are new and generalize some known inequalities in the literatures.     

Conditions for the existence of a solution of a system of differential equations close to an approximate solution

We consider nonautonomous systems of differential equations and state conditions for the existence of an exact solution in a neighborhood of an approximate one by analyzing the linear system of the first approximation in a neighborhood of the constructed approximate solution. We present conditions for the existence of a bounded solution of a linear inhomogeneous system of differential equations.     

一类二阶变系数线性微分方程的积分因子解法

通过寻求积分因子f1(x),f2(x),求解一类二阶线性微分方程,包括二阶常系数线性微分方程和二阶Euler方程.     

Can a solution of a linear delay differential equation have an infinite number of isolated zeros on a finite interval?

A solution of a linear delay differential equation can have an infinite number of isolated zeros on a finite interval. As is well known, for ordinary differential equations this is impossible.     

On the existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process

We study the problem of existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process. For the conditional mathematical expectation of a solution, we obtain a partial differential equation.     

On a theorem of Favard

We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.

     

Construction of a system of linear differential equations from a scalar equation

As is well known, given a Fuchsian differential equation, one can construct a Fuchsian system with the same singular points and monodromy. In the present paper, this fact is extended to the case of linear differential equations with irregular singularities.     

一类二阶变系数线性微分方程的解法

介绍如何通过变换把二阶变系数线性微分方程转化为一阶非线性微分方程,进而利用待定系数法对其求解,并对二阶变系数线性微分方程与一阶常系数非线性微分方程的内在的关系进行讨论.     

Oscillation criteria for a forced mixed type Emden-Fowler equation with impulses

Some oscillation criteria for a forced mixed type Emden-Fowler equation with impulses are given. When the impulses are dropped, our results extend those of Sun and Meng [Y.G. Sun, F.W. Meng, Interval criteria for oscillation of second-order differential equations with mixed nonlinearities, Appl. Math. Comput. 15 (2008) 375-381], Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549-560] for second-order forced ordinary differential equation with mixed nonlinearities, Nasr [A.H. Nasr, Sufficient conditions for the oscillation of forced superlinear second order differential equations with oscillatory potential, Proc. Am. Math. Soc. 126 (1998) 123-125], Yang [Q. Yang, Interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential, Appl. Math. Comput. 135 (2003) 49-64] for forced superlinear Emden-Fowler equation, Kong [Q. Kong, Interval criteria for oscillation of second-order linear differential equations, J. Math. Anal. Appl. 229 (1999) 483-492] for unforced second order linear differential equations, and Wong [J.S.W. Wong, Oscillation criteria for a forced second order linear differential equation, J. Math. Anal. Appl. 231 (1999) 235-240] for forced second order linear differential equation.     

Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations

Aequationes mathematicae - We consider $$3\times 3$$ partially hyperbolic linear differential systems over an ergodic flow $$X^t$$ and derived from the linear homogeneous differential equation...     

Toward a solution of a class of non-linear stochastic perturbed PDEs using automated WHEP algorithm

This paper introduces a generalization and automation of the Wiener Hermite expansion with perturbation (WHEP) technique to solve a class of stochastic nonlinear partial differential equations with a perturbed nonlinearity. The automated algorithm generates the deterministic resultant linear equations according to the application of a general linear differential operator and the input parameters. Sample output with different nonlinearities, orders and corrections are presented. The resultant equations are solved numerically and the ensemble average and variance are computed and compared with previous research work. Higher order solutions with higher corrections are computed to show the importance of the generalization of the WHEP technique. The current work extends the use of WHEP for solving stochastic nonlinear differential equations.     

某类线性微分方程亚纯解的增长性

研究了一类亚纯函数系数的线性微分方程的解的增长性问题,得到了齐次和非齐线性微分方程亚纯解的增长级、超级、二级不同零点收敛指数的精确估计．     

An entire function and its derivatives sharing a polynomial

In this paper, we study the growth of solutions of a first-order linear differential equation and that of a second-order linear differential equation. From this we obtain some uniqueness theorems of a nonconstant entire function and its first derivative having the same fixed points with the same multiplicities. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible.     

A necessary condition for a power series to be a formal solution of a singular linear differential equation of order k

We obtain a necessary condition on the coefficients of a formal power series, which is a formal solution of a nontrivial singular linear differential equation of order k, with analytic coefficients and prove a “uniqueness” theorem for the differential equation.     

Quadratic systems with a linear reflecting function

We construct a set of nonautonomous differential systems with quadratic right-hand side and with a linear reflecting function. We also construct a set of systems whose reflecting function coincides with that of a linear autonomous system.     

一类二阶线性时变系统的稳定性

本文讨论了一类二阶线性时变系统在临界情况下的稳定性，给出了保证该系统零解稳定的充分条件，这一结果将拓宽控制论中二维线性时变控制系统的研究范围。     

Strain of a flexible orthotropic cylindrical shell as a function of orthotropy parameters

A procedure is proposed for calculating the stress-strain state of flexible orthotropic cylindrical shells of constant thickness with unsymtnetric load and nonhomogeneous boundary conditions. The system of nonlinear partial differential equations is solved by the method of lines. The system of nonlinear ordinary differential equations is reduced by linearization to a sequence of linear systems. The sequence of linear boundary-value problems is solved by the discrete orthogonalization method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 57–61, 1986.