一类非线性中立型分数阶泛函微分方程正解的存在性(英文)

本文考虑一类非线性中立型分数阶泛函微分方程.利用锥拉伸与锥压缩不动点定理对问题进行讨论,得到了这类中立型分数阶泛函微分方程正解的存在性.     

泛函微分方程多个正周期解的存在性

考虑一类一阶非线性泛函微分方程,利用锥中的不动点理论给出存在多个正周期解的一些新的充分条件.     

具p-Laplace算子的分数阶微分方程边值问题的正解

考虑具有p-Laplace算子的分数阶泛函微分方程边值问题,利用锥上的不动点定理,得到了其正解及多个正解存在的充分条件,所得结果推广了已有的结论,并举例说明了结论的适用性.     

Banach 空间中分数阶微分方程$m$点边值问题的正解

该文在Banach空间中研究一类分数阶微分方程$m$点边值问题, 证明了格林函数的性质, 构造一个特殊的锥,利用锥拉伸压缩不动点定理得到了该边值问题正解的存在性,最后给出一个例子用以说明主要结果.     

一类非线性共形分数阶微分方程的边值问题和脉冲初值问题（英文）

本文研究一类非线性共形分数阶微分方程的边值问题和脉冲初值问题,利用基于锥理论的和型算子不动点定理和混合单调算子不动点定理,获得共形分数阶微分方程边值问题和脉冲初值问题正解的存在性和唯一性定理,并且得到一组可以逼近唯一正解的单调迭代序列,最后给出一个实例用来验证结论的有效性.     

泛函延拓方法在分数阶常微分方程中的应用

应用线性泛函分析课程中泛函延拓的思想方法结合分数阶常微分方程理论以及Schauder不动点定理,获得了分数阶常微分方程初值问题解的局部存在性以及爆破二择一结果.     

一类带有偏差量及两个参数的非线性分数阶积分边值问题的正解及其性质

本文研究一类分数阶非线性微分方程边值问题,其中微分方程里含有一个偏差量和一个参数,且边界条件中含有一个非线性积分项及一个扰动参数.利用锥理论及带有参数的算子不动点定理获得了该边值问题存在唯一正解的充分条件,并讨论了唯一正解对参数的连续依赖性.作为应用,给出一个具体的例子.     

四阶泛函微分方程边值问题正解的存在性

利用锥拉伸与锥压缩不动点定理,研究了一类四阶泛函微分方程边值问题正解的存在性,得到其正解及多个正解存在的若干充分条件,所得结果是相应常微分方程边值问题已有结论的拓广.     

预解算子控制的无穷时滞分数阶微分方程解的存在性

本文研究了一类预解算子控制的具有无穷时滞的分数阶泛函微分方程.利用解析预解算子理论和不动点定理,得到了具有无穷时滞分数阶微分方程适度解的存在性,推广和改进了一些已知的结果.     

一类无穷区间上分数阶微分方程正解的存在性

讨论一类无穷区间上分数阶微分方程的边值问题,通过构造合适的Green函数,依赖于Green函数的相关性质,利用非线性抉择原理和锥拉压不动点定理,给出了该问题正解的存在性结论.     

Oscillation of Third-order Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.     

非线性中立型泛函微分方程Runge-Kutta 法的稳定性和收敛性

本文涉及Runge-Kutta 法变步长求解非线性中立型泛函微分方程(NFDEs) 的稳定性和收敛性.为此, 基于Volterra 泛函微分方程Runge-Kutta 方法的B- 理论, 引入了中立型泛函微分方程Runge-Kutta 方法的EB (expanded B-theory)-稳定性和EB-收敛性概念. 之后获得了Runge-Kutta 方法变步长求解此类方程的EB - 稳定性和EB- 收敛性. 这些结果对中立型延迟微分方程和中立型延迟积分微分方程也是新的.     

An iterative method for solving nonlinear functional equations

An iterative method for solving nonlinear functional equations, viz. nonlinear Volterra integral equations, algebraic equations and systems of ordinary differential equation, nonlinear algebraic equations and fractional differential equations has been discussed.     

On the Cauchy type problem for systems of functional differential equations

Using theorems on functional differential inequalities, we establish new efficient conditions for the solvability as well as unique solvability of the Cauchy type problem for systems of functional differential equations in both linear and nonlinear cases.     

Nonlinear oscillation of fourth order functional differential equations

Summary In the oscillation theory of nonlinear differential equations one of the important problems is to find necessary and sufficient conditions for the equations under consideration to be oscillatory. Beginning with the pionearing work of F. V. Atkinson, there have been a number of papers. Recently, Kusano and Naito proved the interesting results to the jourth order nonlinear ordinary differential equations of the from [r(t)y″(t)]″+y(t)F(y(t) ₂ ,t)=0. In the present paper, we will extend them to the more general functional differential equations and improve the not clear parts of them. Also, we will propose a new simple definition of nonlinearity of the functional differential equations. Entrata in Redazione il 5 settembre 1977.     

Contractivity and exponential stability of solutions to nonlinear neutral functional differential equations in banach spaces

A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.     

On abstract degenerate neutral differential equations

We introduce a new abstract model of functional differential equations, which we call abstract degenerate neutral differential equations, and we study the existence of strict solutions. The class of problems and the technical approach introduced in this paper allow us to generalize and extend recent results on abstract neutral differential equations. Some examples on nonlinear partial neutral differential equations are presented.     

General existence principles for Stieltjes differential equations with applications to mathematical biology

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.     

Some considerations on functional differential equations of advanced type

We prove some comparison results for the periodic boundary value problem related to a first‐order functional differential equation of advanced type. These maximum principles provide uniqueness results for nonlinear differential equations with advanced arguments. By a change of variable, we deduce analogous results for fuctional differential equations with delayed arguments (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Introduction to the theory of functional differential equations and their applications. Group approach

In this work, we give an introduction to the theory of nonlinear functional differential equations of pointwise type on a finite interval, semi-axis, or axis. This approach is based on the formalism using group peculiarities of such differential equations. For the main boundary-value problem and the Euler-Lagrange boundary-value problem, we consider the existence and uniqueness of the solution, the continuous dependence of the solution on boundary-value and initial-value conditions, and the “roughness” of functional differential equations in the considered boundary-value problems. For functional differential equations of pointwise type we also investigate the pointwise completeness of the space of solutions for given boundary-value conditions, give an estimate of the rank for the space of solutions, describe types of degeneration for the space of solutions, and establish conditions for the “smoothness” of the solution. We propose the method of regular extension of the class of ordinary differential equations in the class of functional differential equations of pointwise type. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 8, Functional Differential Equations, 2004.