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Now showing items 1-10 of 36

#### 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 ...

#### 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 ...

#### 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 ...

#### Monotone Method for Equations Describing Transport Phenomena in a Banach Space

(University of Texas at Arlington, 1981-06)

Existence of extremal solutions of initial and boundary value problems (B.V.P. for short) of differential equations in a Banach
space has been recently considered in [2,7] by utilizing monotone iterative method.
A ...

#### Monotone Iterative Technique for Delay Differantial Equations in Abstract Cones

(University of Texas at Arlington, 1982-04)

Monotone iterative technique is developed for delay differential equations
in a Banach space by utilizing the method of upper and lower solutions.

#### 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 ...

#### 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 ...

#### 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 ...

#### Volterra Integral Equations in Abstract Cones and Monotone Iterative Technique

(University of Texas at Arlington, 1983-08)

The objective of this paper is to develop monotone technique for obtaining extremal solutions of Volterra integral equations in abstract Banach spaces via coupled lower and upper quasi-solutions. To generate the iterates, ...

#### Comparison Results for Reaction-Diffusion Equations in a Banach Space

(University of Texas at Arlington, 1979-06)

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 notations] (1.1)
where the constant Q is the heat of reaction; ...