Now showing items 1-20 of 349

    • Comparison Principle and Non Linear Contract in Abstract Spaces 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 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 a Boundary Value Problem for a Class of Differential Equations with a Deviating Argument 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1973-10)
      **Please note that the full text is embargoed** ABSTRACT: Recently, J. Chandra [1] obtained comparison estimates for differential equations with deviating argument (1) [see pdf for notation] on the interval I: to [see ...
    • Existence MD Estimates for Solutions of Nonlinear Equations Near a Branch Point 

      Eisenfeld, Jerome; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1973-12)
      **Please note that the full text is embargoed** ABSTRACT: 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) ...
    • Truncated Circular Normal Distribution with Applications in Ballistics and Meteorology 

      Dyer, Danny D. (University of Texas at ArlingtonDepartment of Mathematics, 1973-12)
      **Please note that the full text is embargoed** ABSTRACT: 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]. ...
    • On Perturbing Lyapunov Functions 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-02)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...
    • Fixed Point Theorems Through Abstract Cones 

      Eisenfeld, Jerome; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-03)
      **Please note that the full text is embargoed** ABSTRACT: A well-known 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 ...
    • Asymptotic Equilibrium of Ordinary Differential Systems in a Banach Space 

      Mitchell, Roger W.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1974-03)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...
    • On the Existence of Solutions of Differential Equations in a Banach Space 

      Eisenfeld, Jerome; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-03)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...
    • Lyapunov-like Vector Functions Using Pointwise Degenerate Systems as Comparison Functions 

      Asner, Bernard A., Jr.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 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 

      Lakshmikantham, V.; Mitchell, Roger W.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 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 ...
    • Differential Equations on Closed Subsets of a Banach Space 

      Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-07)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...
    • On the Redundancy of Monotony Assumption 

      Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-07)
      **Please note that the full text is embargoed** ABSTRACT: It is well known that all the results in integral inequalities of Bellman-Gronwall-Reid type demand an assumption of monotony on the functions involved. Since the ...
    • Existence and Comparison Results for Differential Equations in a Banach Space 

      Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-07)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...
    • A Technic in Perturbation Theory 

      Ladde, G. S.; Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-07)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...
    • On the Method of Vector Lyapunov Functions 

      Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1974-09)
      **Please note that the full text is embargoed** ABSTRACT: The method of vector Lyapunov functions consists of employing several Lyapunov-like functions and the theory of vectorial differential inequalities. This general ...
    • A Polynomial Dual of Partitions 

      Beard, Jacob T. B., Jr.; Dorris, Ann D. (University of Texas at ArlingtonDepartment of Mathematics, 1974-09)
      **Please note that the full text is embargoed** ABSTRACT: Let [see pdf for notation] be a non-negative integral polynomial. The polynomial P(x) is m-graphical, and a multi-graph G a realization of P(x), provided there ...
    • Matrix Fields Over the Integers Modulo m 

      McConnel, Robert M.; Beard, Jacob T. B., Jr. (University of Texas at ArlingtonDepartment of Mathematics, 1974-10)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...
    • On Massera Type Converse Theorem in Terms of Two Different Measures (0) 

      Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1975)
      **Please note that the full text is embargoed** ABSTRACT: The importance of uniform asymptotic stability in studying the stability properties of perturbed motions needs no emphasis. The converse theorem of Massera which ...
    • Fixed Point Theorms of Operators with PPF Dependence in Banach Spaces 

      Bernfeld, Stephen R. (University of Texas at ArlingtonDepartment of Mathematics, 1975)
      **Please note that the full text is embargoed** ABSTRACT: 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] ...
    • On the Existence of Solutions of Differential Equations and Zeros of Operators in K-Banach Spaces 

      Bronson, Evin; Tennison, R. L.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1975)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...