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Now showing items 1-10 of 19

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### Monotone Methods for Nonlinear Boundary Value Problems in Banach Spaces

(University of Texas at Arlington, 1977-12)

Monotone methods have been used to generate multiple solutions of nonlinear boundary value problems for both ordinary and partial differential equations. Keller [10] and Sattinger [13], extending the chord method, considered ...

#### 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 ...

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

(University of Texas at Arlington, 1974-03)

The study of Cauchy problem for differential equations in a Banach space has taken two different directions. One approach is to find compactness type conditions [1,2,4,9,14] to guarantee existence of solutions only and the ...

#### On the Existence of Weak Solutions of Differential Equations in Nonreflexive Banach Spaces

(University of Texas at Arlington, 1977-03)

The study of the Cauchy problem for differential equations in a Banach space relative to the strong topology has attracted much attention in recent years [2,4,5,7]. This study has taken two different directions. One direction ...

#### Differential Equations on Closed Subsets of a Banach Space

(University of Texas at Arlington, 1974-07)

The problem of existence of solutions to the initial value problem [see pdf for notations], where [see pdf for notations], F is a locally closed subset of a Banach space E. Nonlinear comparison functions and dissipative ...