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Now showing items 1-10 of 22

#### 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] ...

#### 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 ...

#### 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; ...

#### On Existence of Extremal Solutions of Differential Equations in Banach Spaces

(University of Texas at Arlington, 1978-06)

Let X be a real Banach space, [see pdf for notation] a cone, [see pdf for notation] and [see pdf for notation] continuous. We look for conditions on X, K and f such that the IVP
(1) [see pdf for notation]
has a maximal ...

#### On the Existence of Solutions of Differential Equations and Zeros of Operators in K-Banach Spaces

(University of Texas at Arlington, 1975)

The theory of existence of solutions of differential equations in a Banach space employing norm as a measure is sufficiently well known [5, 6, 8, 9]. Also utilizing this theory one can prove the existence of zeros of ...

#### On the Existence of Solutions of Differential Equations of Retarded Type in a Banach Space

(University of Texas at Arlington, 1975-06)

The existence and uniqueness of solutions of differential equations of retarded type in a Banach space are considered under a monotonicity type condition. The tools that are available for the study of equations without ...