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Now showing items 1-10 of 41

#### A New Approach to the Method of Nonlinear Variation of Parameters

(University of Texas at Arlington, 1975-01)

As is well-known [3] the method of variation of parameters is a very useful tool in studying the properties of solutions of perturbed differential equations. Extending the classical variation of constants formula for linear ...

#### On the Existence and Uniqueness of Periodic Solutions of Second Order Ordinary Differential Equations

(University of Texas at Arlington, 1979-10)

#### Existence and Comparison Theorems for Differential Equations in Banach Spaces

(University of Texas at Arlington, 1978-07)

In our recent paper [3] we have studied the existence of maximal and minimal solutions to the IVP in a Banach space [see pdf for notation].
(1) [see pdf for notation]
where [see pdf for notation] maps [see pdf for notation] ...

#### A Topological Method for Vector-Valued and Nth Order Nonlinear Boundary Value Problems

(University of Texas at Arlington, 1982-05)

The use of topological methods in the analysts of second order nonlinear boundary value problems (BVP for short) in Rn of the form
(E) [see pdf for notation]
(C) [see pdf for notation]
has recently attracted the interest ...

#### Quasi-Solutions and Their Role in the Qualitative Theory of Differential Equations

(University of Texas at Arlington, 1979-08)

In the study of comparison theorems and extremal solutions for systems of ordinary differential equations [5], one usually imposes a condition on the right hand side known as quasi-monotone nondecreasing property. This ...

#### Stability and Asymptotic Equivalence of Perturbations of Nonlinear Systems of Differential Equations

(University of Texas at Arlington, 1980-08)

A nonlinear variation of constants method was introduced by Alekseev [1] and applications of this formula to questions of stability and asymptotic equivalence of differential systems was demonstrated by Brauer [2,3,4]. In ...

#### Attractivity AMP Hopf Bifurcation

(University of Texas at Arlington, 1978-02)

Consider the one-parameter family of differential equations
[see pdf for notation]
where [see pdf for notation] and [see pdf for notation]. Here [see pdf for notation] and [see pdf for notation]. Denoting by [see pdf for ...

#### Comparison Principle and Non Linear Contract in Abstract Spaces

(University of Texas at Arlington, 1973-10)

The theory of differential and integral equations exploits comparison and iterative techniques which do not fall under the Contractive Mapping Principle. For they make use of partial orderings and maximal solutions; concepts ...

#### Comparison Results for Reaction-Diffusion Equations in a Banach Space

(University of Texas at Arlington, 1979-06)

Let T be the temperature and n the concentration of a combustible substance. A simple model governing the combustion of the material is given by
[see pdf for notations] (1.1)
where the constant Q is the heat of reaction; ...

#### A Quadratic Volterra Integral Equation and Its Solution for Various Kernels

(University of Texas at Arlington, 1997)

Consider the Volterra integral equation [see pdf for notation], ^ is a parameter Solutions of this equation are discussed for separable and difference kernels using Laplace transform and differential equation techniques. ...