## Search

Now showing items 1-10 of 10

#### 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 ...

#### 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; ...

#### On Existence of Extremal Solutions of Differential Equations in Banach Spaces

(University of Texas at Arlington, 1978-06)

Let X be a real Banach space, [see pdf for notation] a cone, [see pdf for notation] and [see pdf for notation] continuous. We look for conditions on X, K and f such that the IVP
(1) [see pdf for notation]
has a maximal ...

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

(University of Texas at Arlington, 1975-06)

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 that are available for the study of equations without ...

#### 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 ...

#### On the Zeros of Monotone Operators of Retarded Type in a Banach Space

(University of Texas at Arlington, 1975-09)

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 type in a Banach space. The difficulty in imposing assumptions ...

#### 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 ...

#### Existence of Solutions of Boundary Value Problems for Nonlinear Second Order Systems in a Banach Space

(University of Texas at Arlington, 1977-03)

This paper is concerned with the existence of solutions of boundary value problems (BVP, for short) for nonlinear second order ordinary differential equations of the type
(1.1) [see pdf for notation]
(1.2) [see pdf for ...

#### Monotone Iterative Technique for Differential Equations in a Banach Space

(University of Texas at Arlington, 1981-02)

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]. Generally speaking of approximate
solutions of (1.1) consist ...

#### Fixed Point Theorems for PPF Mappings Satisfying Inwardness Conditions

(University of Texas at Arlington, 1980-07)

In this paper we continue our recent development [1] of the theory of fixed point theorems of nonlinear operators whose domain and range are different Banach spaces. In particular we consider the analogues of recent results ...