Browsing Department of Mathematics by Issue Date
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On a Boundary Value Problem for a Class of Differential Equations with a Deviating Argument
(University of Texas at ArlingtonDepartment of Mathematics, 197310)Recently, J. Chandra [1] obtained comparison estimates for differential equations with deviating argument (1) [see pdf for notation] on the interval I: to [see pdf for notation] , where [see pdf for notation] is a given ... 
Comparison Principle and Non Linear Contract in Abstract Spaces
(University of Texas at ArlingtonDepartment of Mathematics, 197310)The theory of differential and integral equations exploits comparison and iterative techniques which do not fall under the Contractive Mapping Principle. For they make use of partial orderings and maximal solutions; concepts ... 
Existence MD Estimates for Solutions of Nonlinear Equations Near a Branch Point
(University of Texas at ArlingtonDepartment of Mathematics, 197312)Consider the equation (1.1) [see pdf for notation] on a Hilbert space H. Here n is a scalar and [see pdf for notation] is a linear Fredholm operator. That is: (a) L is closed; (b) The domain, D(L) is dense in H; (c) The ... 
Truncated Circular Normal Distribution with Applications in Ballistics and Meteorology
(University of Texas at ArlingtonDepartment of Mathematics, 197312)The use of the circular normal distribution (CND) to describe the behavior of random phenomena of a geophysical nature has been discussed by Crutcher [7, p. 9]. Based on the Mauchly [17]  Hsu [12] test, the harmonic dial ... 
On Perturbing Lyapunov Functions
(University of Texas at ArlingtonDepartment of Mathematics, 197402)It is known [2,3] that in proving uniform boundedness of a differential system by means of Lyapunov functions, it is sufficient to impose conditions in the complement of a compact set in [see pdf for notation], whereas, ... 
On the Existence of Solutions of Differential Equations in a Banach Space
(University of Texas at ArlingtonDepartment of Mathematics, 197403)The study of Cauchy problem for differential equations in a Banach space has taken two different directions. One approach is to find compactness type conditions [1,2,4,9,14] to guarantee existence of solutions only and the ... 
Asymptotic Equilibrium of Ordinary Differential Systems in a Banach Space
(University of Texas at ArlingtonDepartment of Mathematics, 197403)A differential system [see pdf for notation] where [see pdf for notation] has asymptotic equilibrium if 1) for any initial condition [see pdf for notation] the system has a solution [see pdf for notation] existing on and ... 
Fixed Point Theorems Through Abstract Cones
(University of Texas at ArlingtonDepartment of Mathematics, 197403)A wellknown theorem of Banach states that if T is a mapping on a complete metric space [see pdf for notation] such that for some number [see pdf for notation], the inequality (1.1) [see pdf for notation] holds, then T has ... 
Maximal and Minimal Solutions and Comparison Results for Differential Equations in Abstract Cones
(University of Texas at ArlingtonDepartment of Mathematics, 197404)As is well known, an important technique in the theory of differential equations is concerned with estimating a function satisfying a differential inequality by means of the extremal solutions of the corresponding differential ... 
Lyapunovlike Vector Functions Using Pointwise Degenerate Systems as Comparison Functions
(University of Texas at ArlingtonDepartment of Mathematics, 197404)The use of Lyapunovlike vector functions is recognized as an important tool for estimating the behavior of a dynamical system. In applications, one needs to determine a suitable comparison function which contains information ... 
Existence and Comparison Results for Differential Equations in a Banach Space
(University of Texas at ArlingtonDepartment of Mathematics, 197407)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 that guarantee only existence of solutions and the ... 
Differential Equations on Closed Subsets of a Banach Space
(University of Texas at ArlingtonDepartment of Mathematics, 197407)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 space E. Nonlinear comparison functions and dissipative ... 
On the Redundancy of Monotony Assumption
(University of Texas at ArlingtonDepartment of Mathematics, 197407)It is well known that all the results in integral inequalities of BellmanGronwallReid type demand an assumption of monotony on the functions involved. Since the corresponding theory of differential inequalities does not ... 
A Technic in Perturbation Theory
(University of Texas at ArlingtonDepartment of Mathematics, 197407)A study of the effect of perturbations of differential equations depends on the method employed and on the nature of perturbations. One of the most used technics is that of Lyapunov method and the other is the nonlinear ... 
On the Method of Vector Lyapunov Functions
(University of Texas at ArlingtonDepartment of Mathematics, 197409)The method of vector Lyapunov functions consists of employing several Lyapunovlike functions and the theory of vectorial differential inequalities. This general comparison technic leads to a more flexible mechanism to ... 
A Polynomial Dual of Partitions
(University of Texas at ArlingtonDepartment of Mathematics, 197409)Let [see pdf for notation] be a nonnegative integral polynomial. The polynomial P(x) is mgraphical, and a multigraph G a realization of P(x), provided there exists a multigraph G containing exactly P(1) points where ... 
Matrix Fields Over the Integers Modulo m
(University of Texas at ArlingtonDepartment of Mathematics, 197410)Let Zm denote the ring of integers modulo m and let [see pdf for notation] denote the complete ring of all [see pdf for notation] matrices over Zm under the usual matrix addition and multiplication. The primary purposes ... 
Fixed Point Theorms of Operators with PPF Dependence in Banach Spaces
(University of Texas at ArlingtonDepartment of Mathematics, 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 ... 
On Massera Type Converse Theorem in Terms of Two Different Measures (0)
(University of Texas at ArlingtonDepartment of Mathematics, 1975)The importance of uniform asymptotic stability in studying the stability properties of perturbed motions needs no emphasis. The converse theorem of Massera which results from uniform asymptotic stability has been widely ... 
On the Existence of Solutions of Differential Equations and Zeros of Operators in KBanach Spaces
(University of Texas at ArlingtonDepartment of Mathematics, 1975)The theory of existence of solutions of differential equations in a Banach space employing norm as a measure is sufficiently well known [5, 6, 8, 9]. Also utilizing this theory one can prove the existence of zeros of ...