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Now showing items 1-10 of 11

#### On the Existence of Zeros of Lyapunov-Monotone Operators

(University of Texas at Arlington, 1975-02)

Consider a nonlinear operator T from a Banach space into itself.
The study of the existence of zeros of T plays an important role in yielding fixed points of nonlinear operators. The operator T has a zero if and only if ...

#### Existence and Monotone Method for Periodic Solutions of First Order Differential Equations

(University of Texas at Arlington, 1981-09)

An attempt was made recently in [3] to combine fruitfully the two basic techniques, namely the method of upper and lower solutions and the Lyapunov-Schmitt
method to investigate the existence of periodic solutions of ...

#### Existence and Uniqueness of Solutions of Delay Differential Equations on a Closed Subset of a Banach Space

(University of Texas at Arlington, 1977-05)

In an earlier work [5], sufficient conditions for the existence of solutions in a closed subset F of a Banach space E for the Cauchy problem
(1.1) [see pdf for notation]
where [see pdf for notation],
are obtained by ...

#### Cone-Valued Lyapunov Functions

(University of Texas at Arlington, 1976-08)

It is very well known that employing a single
Lyapunov function and the theory of scalar
differential inequality offers a useful
mechanism to study a variety of qualitative
problems of differential equations ...

#### On the Method of Upper and Lower Solutions in Abstract Cones

(University of Texas at Arlington, 1981-02)

#### Quasi-Solutions, Vector Lyapunov Functions and Monotone Method

(University of Texas at Arlington, 1980-02)

It is now well known that the method of vector Lyapunov functions provides an effective tool to investigate the properties of large scale
interconnected dynamical and control systems. [3,4,5,11-15]. Several Lyapunov ...

#### Method of Quasi-Upper and Lower Solutions in Abstract Cones

(University of Texas at Arlington, 1981-05)

Let E be a real Banach space with ||•|| and let E* denote the dual of E. Let K C E be a cone, that is, a closed convex subset such
that ^K C K for every ^ ≥ 0 and K ^ {-K} = {O}, By means of K a partial order ≤ is defined ...

#### A Technic in Perturbation Theory

(University of Texas at Arlington, 1974-07)

A study of the effect of perturbations of differential equations depends on the method employed and on the nature of perturbations. One of the most used technics is that of Lyapunov method and the other is the nonlinear ...

#### A Monotone Method for Infinite System of Nonlinear Boundary Value Problems

(University of Texas at Arlington, 1976-08)

Monotone iterative methods have been successfully used to generate improvable two-sided point-wise bounds on solutions of nonlinear boundary value problems for both ordinary and partial differential equations. While such ...

#### A Technique in Stability Theory of Delay-Differential Equations

(University of Texas at Arlington, 1978-04)

In the study of stability theory for delay-differential equations using Lyapunov functions and the theory of differential inequalities, it becomes necessary to choose an appropriate minimal class of functions relative to ...