Positive solutions for systems of nonlinear eigenvalue problems for functional differential equations

Values of?λ?are determined for which there exist positive solutions of the system of functional differential equations, u″?+?λa(t)f(v _t )?=?0,v″?+?λb(t)g(u _t )?=?0, for 0?t?u(s)?=?v(s)?=?φ(s), ?r?≤?s?≤?0, and the boundary conditions u(0)?=?v(0)?=?φ(0)?=?u(1)?=?v(1)?=?0. A Guo–Krasnosel'skii fixed point theorem is applied.     

Discontinuous first-order functional boundary value problems

In this paper we prove a new existence result for functional boundary value problems with first-order functional differential equations under weak conditions on the nonlinear part and monotonicity (but not continuity) with respect to the functional variable. Discontinuities with respect to the unknown are allowed to occur over general classes of time-dependent sets which are assumed to satisfy a kind of unviability or solubility condition.     

On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals

We study the existence of positive solutions for the following boundary value problem on infinite interval for second-order functional differential equations:

     

Approximation of nonlinear functional differential equation control systems

We develop a general approximation framework for use in optimal control problems governed by nonlinear functional differential equations. Our approach entails only the use of linear semigroup approximation results, while the nonlinearities are treated as perturbations of a linear system. Numerical results are presented for several simple nonlinear optimal control problem examples.This research was supported in part by the US Air Force under Contract No. AF-AFOSR-76-3092 and in part by the National Science Foundation under Grant No. NSF-GP-28931x3.     

Inequalities and stability for a linear scalar functional differential equation

There have been a lot of investigations about stability of the linear scalar functional differential equation

x′(t)=a(t)x(t)+b(t)x(t−h),     

二阶奇异泛函微分方程的两点边值问题

本文研究具有Ｒｏｂｉｎ边界条件的二阶奇异泛函微分方程组Ａ（ｔ,ｘ,ｘ）ｘ＝ｆ（ｔ,ｘｔ,ｘｔ）的两点边值问题,给出该两点边值问题的两个解的先验估计定理和一个解的存在定理．     

Nonoscillations for odd-dimensional systems of linear retarded functional differential equations

This paper is concerned with the nonoscillatory problems of odd-dimensional systems of linear retarded functional differential equations. Based upon the corresponding characteristic equations, we get some criteria for nonoscillations by utilizing the matrix measures.     

Multiple positive solutions for a functional second-order boundary value problem

By using the Krasnoselskii fixed point theorem on cones in Banach spaces some existence results of positive solutions of a boundary value problem concerning a second-order functional differential equation are given.     

Nonlocal boundary value problems for second-order functional differential equations

We study the existence of a solution to a nonlocal boundary value problem for a class of second-order functional differential equations with piecewise constant arguments. The equation studied includes terms depending on the derivative as well as delay arguments in the derivative.     

Boundary value problems for higher order linear impulsive differential equations

In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green's formula is defined for piecewise differentiable functions. Properties of Green's functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green's function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered.     

Multipoint boundary value problems of Neumann type for functional differential equations

We obtain the expression of the explicit solution to a class of multipoint boundary value problems of Neumann type for linear ordinary differential equations and apply these results to study sufficient conditions for the existence of solution to linear functional differential equations with multipoint boundary conditions, considering the particular cases of equations with delay and integro-differential equations.     

A discontinuous functional differential equation

In this paper we give a sufficient condition for the existence of maximal and minimal solutions to a discontinuous functional differential equation x′(t)=f(t,x(t),x(·)), x(0)=0. We apply the result to establish an existence theorem for the Darboux problem for a partial differential equation.     

Second-order functional differential equations with past, present and future dependence

In this paper we obtain a result on existence of extremal quasisolutions and solutions for second-order functional differential equations with functional boundary conditions and past, present and future dependence. In order to do that, we develop a generalized monotone method in presence of lower and upper solutions. Some examples of application are provided too.     

Existence of positive solution for singular fractional differential equation

In this paper, we establish the existence of a positive solution to a singular boundary value problem of nonlinear fractional differential equation. Our analysis rely on nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem in a cone.     

Analytic solutions of an iterative functional differential equation

This paper is concerned with a functional differential equation x^′(z)=1/x(az+bx(z)), where a, b are two complex numbers. By constructing a convergent power series solution y(z) of a auxiliary equation of the form b²y^′(z)=(y(μ²z)−ay(μz))(μy^′(μz)−ay^′(z)), analytic solutions of the form for the original differential equation are obtained.     

Alternative solution of the inhomogeneous linear differential equation of order two

In this paper, we present an alternative method for solving the general inhomogeneous linear ordinary differential equation (ODE) of order two. The solution appears in the standard form as the sum of the solution of the equivalent homogeneous problem and the particular solution of the inhomogeneous problem at hand. The main advantage of the method exposed herein is that the particular solution is computable from two different integrals. This allows the problem solver to choose the simplest integral with which to work with in order to get the final solution. For illustrative purposes we employ the method presented to aid in the solution of some example problems including the inhomogeneous Klein-Gordon equation.     

Non-linear functional boundary value problem for discontinuous functional differential equations

This paper is devoted to investigating the existence of solutionsfor discontinuous functional differential equations with non-linearfunctional boundary conditions. Some existence results of solutionsare obtained by employing a generalized method of upper andlower solutions, which may be discontinuous.