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Now showing items 1-10 of 15

#### Monotone Technique for Periodic Solutions of Differential Equations

(University of Texas at Arlington, 1982-07)

The existence of periodic solutions has received
a great deal of attention in recent years [1,7-11,14]. In [8,11] the existence of solutions of first
and second order PBVP (periodic boundary
value problem) has ...

#### 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 ...

#### Stability of Differential Systems with Impulsive Perturbations in Terms of Two Measures

(University of Texas at Arlington, 1977-01)

The study of differential systems of the form
(1.1) [see pdf for notation]
where [see pdf for notation] denotes the distributional derivative of [see pdf for notation], a function of bounded variation (that is, differential ...

#### 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 ...

#### Existence of Solutions in a Closed Set for Delay Differential Equations in Banach Spaces

(University of Texas at Arlington, 1977-01)

The study of the Cauchy problem for ordinary differential equations
in a Banach space has been extensive [1,3-7,9-12]. The two main directions that are followed in such a study are (i) finding monotonicity type conditions ...