一阶非线性具偏差变元脉冲微分方程

给出了具有时滞和时超的一阶非线性脉冲微分方程所有解为振动的充分条件，所得结论包含了线性情形作为其推论。     

Systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions

This paper is concerned with the existence of solutions for systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions. By establishing new comparison results and applying the monotone iterative technique, we obtain the sufficient conditions for the existence of extremal system of solutions.     

Existence of positive periodic solutions of first‐order neutral differential equations

This paper presents the existence of positive periodic solutions for first‐order neutral differential equation with distributed deviating arguments. We apply Krasnoselskii's fixed point theorem to obtain our results. An example is given to support the theory. Copyright © 2016 John Wiley & Sons, Ltd.     

On a periodic problem for higher-order differential equations with a deviating argument

For higher-order nonautonomous linear and nonlinear differential equations with deviating arguments, new sufficient conditions of existence and uniqueness of a periodic solution are found.     

OSCILLATION CRITERIA FOR HIGHER-ORDER IMPULSIVE HYPERBOLIC SYSTEM WITH DISTRIBUTED DEVIATING ARGUMENTS

By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Robin and Dirichlet boundary value conditions.     

Impulsive stability for systems of second order retarded differential equations

This paper is concerned with systems of impulsive second order delay differential equations. We prove that unstable systems can be stabilized by imposition of impulsive controls. The main tools used are Lyapunov functionals, stability theory and control by impulses.     

一类二阶中立型偏泛函微分方程的振动性

获得了一类具连续偏差变元二阶非线性中立型偏微分方程的振动性的充分性条件.     

一类二阶时滞泛函微分方程的振动性和渐进性

本文简介了时滞泛函微分方程的研究现状和主要方法 ,并对一类二阶非线性时滞泛函微分方程的振动性和渐近性进行了研究 ,给出该类方程振动性的一个充分条件 .     

Solvability of three point boundary value problems for second order differential equations with deviating arguments

The monotone iterative technique is used to boundary problems for second order ordinary differential equations with deviating arguments. Corresponding results are formulated when the problem has extremal solutions or weakly coupled extremal quasi-solutions.     

带强迫项的二阶泛函微分方程解的振动性和渐近性

该文建立了偏差变元依赖于状态的二阶强迫泛函微分方程解的若干振动和渐近性质 ,所得结果推广和改进了文献中的有关结果     

A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL INEQUALITIES WITH DISTRIBUTED TYPE DEVIATING ARGUMENTS

ＡＣＬＡＳＳＯＦＳＥＣＯＮＤＯＲＤＥＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＩＮＥＱＵＡＬＩＴＩＥＳＷＩＴＨＤＩＳＴＲＩＢＵＴＥＤＴＹＰＥＤＥＶＩＡＴＩＮＧＡＲＧＵＭＥＮＴＳ（傅希林）￥ＦｕＸｉｌｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｈａｎｄｏｎｇＮｏｒ...     

Nagumo type existence results of Sturm-Liouville BVP for impulsive differential equations

In this paper, the method of upper and lower solutions and the Schauder degree theory are employed in the study of Sturm-Liouville boundary value problems for second order impulsive differential equations. We obtain the existence of at least three solutions to the problem under the assumption that the nonlinear term f satisfies a Nagumo condition with respect to the first order derivative.     

Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating Arguments

This paper considers fourth-order differential equations with four-point boundary conditions and deviating arguments. We establish sufficient conditions under which such boundary-value problems have positive solutions. We discuss such problems in the cases when the deviating arguments are delayed or advanced. In order to obtain the existence of at least three positive solutions, we use a fixed-point theorem due to Avery and Peterson. To the authors’ knowledge, this is a first paper where the existence of positive solutions of boundary-value problems for fourth-order differential equations with deviating arguments is discussed.     

Coupled fixed points of multivalued operators and first-order ODEs with state-dependent deviating arguments

We establish a coupled fixed point theorem for a meaningful class of mixed monotone multivalued operators, and then we use it to derive some results on the existence of quasisolutions and unique solutions to first-order functional differential equations with state-dependent deviating arguments. Our results are very general and can be applied to functional equations featuring discontinuities with respect to all of their arguments, but we emphasize that they are new even for differential equations with continuously state-dependent delays.     

Integral boundary value problems for first order integro-differential equations with deviating arguments

This paper deals with first order integro-differential equations of mixed type with deviating arguments. We investigate the existence of solutions of such problems with integral boundary conditions by establishing a comparison result and applying the monotone iterative technique. To obtain corresponding results, we also discuss first order differential inequalities with deviating arguments. Two examples demonstrate the application of our results.     

Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions

In this paper, the existence of at least three positive solutions to impulsive second order differential equations is investigated. Sufficient conditions which guarantee the existence of positive solutions are obtained, by using the Avery-Peterson theorem. An example is added to illustrate the results.     

Further results on oscillation of a class of second-order neutral equations

This paper establishes several results on oscillation of a class of second neutral differential equations with distributed deviating arguments.     

具有偏差变元的二阶泛函微分方程周期解的存在性

该文利用k- 集压缩算子抽象连续性定理和一些分析技巧研究了一类具有偏差变元的二阶泛函微分方程周期解的存在性. 该文的结果推广和改进了文献[1-2]的主要结果.     

Localization Results for Impulsive Second Order Coupled Systems on the Half-Line and Application to Logging Timber by Helicopter

This work considers two types of a second order impulsive coupled system of differential equations with generalized jump conditions in half-line. For both problems it will be presented two localization results with different monotonicity assumptions on the nonlinearities and on the impulsive conditions.

The arguments apply lower and upper solutions method combined with Nagumo type condition and truncature techniques.

Last section contains an applications of one of this impulsive problems to logging timber by helicopter.

     

Oscillation of Differential Equations with Deviating Arguments

1.IntroductionConsiderthefirstorderdifferentialequationwithdeviatingargumentoftheformX'(t) p(t)x(T(t))~0,t2to(1)where,p,reC([t,' co),R),tim,-ocr(t)~~andrisnondecreasingon[t,,co))'TheoscillatorybehaviourofsolutionsofEq.(1)hasbeeninvestigatedbythanyauthors.WerefertothemonographsbyErbe,KongandZhang[fi,andthepapers[2--6j.Mostoftheknownresults,however,dealwithequationswithretardedoradvancedarguments.ConsiderablylessisknownaboutthebehaviourofthesolutionsofEq.(1)whenitisofmixedtype,thatis,thedevi…