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Now showing items 1-10 of 17

#### 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 ...

#### Stability and Generalized Hopf Bifurcation Through a Reduction Principle

(University of Texas at Arlington, 1980-10)

We are interested in obtaining an analysis of the bifurcating periodic orbits arising in the generalized Hopf bifurcation problems in Rn. The existence of these periodic orbits has often been obtained by using such techniques ...

#### Generalized Hopf Bifurcation and h-Asymptotic stability

(University of Texas at Arlington, 1979-11)

The prevalent approach to the Hopf bifurcation problem is to prove directly the existence of the bifurcating periodic orbits by using such standard
procedures as the implicit function theorem, the LiapunovSchmidt method ...

#### Practical Stability and Lyapunov Functions

(University of Texas at Arlington, 1979-10)

The notion of "practical stability" was discussed in the monograph by LaSalle and Lefschetz [6] in which they point out that stability investigations
may not assure "practical stability" and vice versa. For example an ...

#### The Extendability and Uniqueness of Solutions of Ordinary Differential Equations

(University of Texas at Arlington, 1976)

In a recent paper [1] the author obtained results on the extendability of solutions of perturbed differential equations. The question of the extendability of solutions of differential equations is a fundamental and important ...

#### Fixed Point Theorms of Operators with PPF Dependence in Banach Spaces

(University of Texas at Arlington, 1975)

In this paper we develop a theory of fixed points of a nonlinear operator, T, whose domain is the Banach space of continuous functions defined on an interval [a,b] with range in a Banach space E denoted by [see pdf for ...

#### Generalized Hopf Bifurcation in Rn and h-Asymptotic Stability

(University of Texas at Arlington, 1979-10)

#### Linear Monotone Method for Nonlinear Boundary Value Problems in Banach Spaces

(University of Texas at Arlington, 1981-05)

One of the most useful techniques in proving the existence of multiple solutions of nonlinear boundary value problems (BVP for short) is the
monotone iterative method, which yields monotone sequences that converge to ...

#### A Topological Method for Vector-Valued and Nth Order Nonlinear Boundary Value Problems

(University of Texas at Arlington, 1982-05)

The use of topological methods in the analysts of second order nonlinear boundary value problems (BVP for short) in Rn of the form
(E) [see pdf for notation]
(C) [see pdf for notation]
has recently attracted the interest ...

#### 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 ...