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Block Diagonalization and Eigenvalues
(University of Texas at Arlington, 1975-03)
**Please note that the full text is embargoed** ABSTRACT: Let A denote an Algebra with an identity element. Consider an [see pdf for notation] matrix [see pdf for notation] with a partitioning [see pdf for notation] where ...
Differential Equations on Closed Subsets of a Banach Space
(University of Texas at Arlington, 1974-07)
**Please note that the full text is embargoed** ABSTRACT: 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 ...
On the Existence of Zeros of Lyapunov-Monotone Operators
(University of Texas at Arlington, 1975-02)
**Please note that the full text is embargoed** ABSTRACT: 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 ...
On the Redundancy of Monotony Assumption
(University of Texas at Arlington, 1974-07)
**Please note that the full text is embargoed** ABSTRACT: It is well known that all the results in integral inequalities of Bellman-Gronwall-Reid type demand an assumption of monotony on the functions involved. Since the ...
On the Method of Vector Lyapunov Functions
(University of Texas at Arlington, 1974-09)
**Please note that the full text is embargoed** ABSTRACT: The method of vector Lyapunov functions consists of employing several Lyapunov-like functions and the theory of vectorial differential inequalities. This general ...
Existence of Solutions of Boundary Value Problems for Nonlinear Second Order Systems in a Banach Space
(University of Texas at Arlington, 1977-03)
**Please note that the full text is embargoed** ABSTRACT: This paper is concerned with the existence of solutions of boundary value problems (BVP, for short) for nonlinear second order ordinary differential equations of ...
On the Existence of Weak Solutions of Differential Equations in Nonreflexive Banach Spaces
(University of Texas at Arlington, 1977-03)
**Please note that the full text is embargoed** ABSTRACT: 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]. ...
Differential Inequalities and Flow-Invariance via Linear Functionals
(University of Texas at Arlington, 1977-05)
**Please note that the full text is embargoed** ABSTRACT: This paper deals with flow-invariance properties with respect to [see pdf for notation] and resulting comparison inequalities. Both the order relation He and the ...
Existence and Comparison Results for Differential Equations in a Banach Space
(University of Texas at Arlington, 1974-07)
**Please note that the full text is embargoed** ABSTRACT: 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 ...
A New Approach to the Method of Nonlinear Variation of Parameters
(University of Texas at Arlington, 1975-01)
**Please note that the full text is embargoed** ABSTRACT: 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 ...