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Comparison Principle and Non Linear Contract in Abstract Spaces
(University of Texas at Arlington, 1973-10)
**Please note that the full text is embargoed** ABSTRACT: The theory of differential and integral equations exploits comparison and iterative techniques which do not fall under the Contractive Mapping Principle. For they ...
On the Existence of Solutions of Differential Equations of Retarded Type in a Banach Space
(University of Texas at Arlington, 1975-06)
**Please note that the full text is embargoed** ABSTRACT: The existence and uniqueness of solutions of differential equations of retarded type in a Banach space are considered under a monotonicity type condition. The tools ...
Comparison Results for Reaction-Diffusion Equations in a Banach Space
(University of Texas at Arlington, 1979-06)
**Please note that the full text is embargoed** ABSTRACT: Let T be the temperature and n the concentration of a combustible substance. A simple model governing the combustion of the material is given by
[see pdf for ...
On the Zeros of Monotone Operators of Retarded Type in a Banach Space
(University of Texas at Arlington, 1975-09)
**Please note that the full text is embargoed** ABSTRACT: Recent interest in the Cauchy problem for differential equations in a Banach space [9] has stimulated a similar interest for differential equations of a retarded ...
Lyapunov-like Vector Functions Using Pointwise Degenerate Systems as Comparison Functions
(University of Texas at Arlington, 1974-04)
**Please note that the full text is embargoed** ABSTRACT: The use of Lyapunov-like vector functions is recognized as an important tool for estimating the behavior of a dynamical system. In applications, one needs to determine ...
Maximal and Minimal Solutions and Comparison Results for Differential Equations in Abstract Cones
(University of Texas at Arlington, 1974-04)
**Please note that the full text is embargoed** ABSTRACT: As is well known, an important technique in the theory of differential equations is concerned with estimating a function satisfying a differential inequality by ...
Monotone Iterative Technique for Differential Equations in a Banach Space
(University of Texas at Arlington, 1981-02)
**Please note that the full text is embargoed** ABSTRACT: Let E be a real Banach space with norm [see pdf for notation].
Consider the initial value problem (1.1) [see pdf for notation],
where [see pdf for notation]. ...
Existence and Comparison Results for a Class of Volterra Integral Equations of Sobolev Type
(University of Texas at Arlington, 1978-09)
**Please note that the full text is embargoed** ABSTRACT: Recently [2] a class of new differential equations called Sobolev type differential equations was introduced and Picard type existence theorem for such equations ...
Maximal and Minimal Solutions and Comparison Principle for Differential Equations in Abstract Cones
(University of Texas at Arlington, 1975-06)
**Please note that the full text is embargoed** ABSTRACT: Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result ...
On a Measure of Nonconvexity and Applications
(University of Texas at Arlington, 1975-06)
**Please note that the full text is embargoed** ABSTRACT: The measure of noncompactness which was introduced by Kuratowski [8] (in 1930) has now become an important tool in nonlinear analysis (although its value in that ...