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Now showing items 1-10 of 42

#### On the Construction of a Norm Associated with the Measure of Noncompactness

(University of Texas at Arlington, 1976-02)

It is shown that the bounded, nonempty subsets of a reflexive Banach space g can be imbedded in another Banach space B(E) in such a manner so that the measure of noncompactness corresponds to the norm in B(E). The results ...

#### Stochastic Differential Inequalities of Ito Type

(University of Texas at Arlington, 1978-06)

It is well known [3] that the method of differential inequalities plays an important role in the qualitative theory of differential equations. It is therefore natural to expect that a similar theory would be equally important ...

#### On the Method of Vector Lyapunov Functions

(University of Texas at Arlington, 1974-09)

The method of vector Lyapunov functions consists of employing several Lyapunov-like functions and the theory of vectorial differential inequalities. This general comparison technic leads to a more flexible mechanism to ...

#### 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 ...

#### Maximal and Minimal Solutions and Comparison Results for Differential Equations in Abstract Cones

(University of Texas at Arlington, 1974-04)

As is well known, an important technique in the theory of differential equations is concerned with estimating a function satisfying a differential inequality by means of the extremal solutions of the corresponding differential ...

#### On a Boundary Value Problem for a Class of Differential Equations with a Deviating Argument

(University of Texas at Arlington, 1973-10)

Recently, J. Chandra [1] obtained comparison estimates for differential equations with deviating argument
(1) [see pdf for notation]
on the interval I: to [see pdf for notation] , where [see pdf for notation] is a given ...

#### The Method of Quasilinearization and Positivity of Solutions in Abstract Cones

(University of Texas at Arlington, 1976-03)

The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the method can be found in (Ref. 3). This method has been very ...

#### Practical Stability and Lyapunov Functions

(University of Texas at Arlington, 1979-10)

The notion of "practical stability" was discussed in the monograph by LaSalle and Lefschetz [6] in which they point out that stability investigations
may not assure "practical stability" and vice versa. For example an ...

#### Existence and Comparison Results for Differential Equations in a Banach Space

(University of Texas at Arlington, 1974-07)

The study of the Cauchy problem for differential equations in a Banach space has taken two different directions. One direction is to find compactness type conditions that guarantee only existence of solutions and the ...

#### 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 ...