Browsing by Author "Lakshmikantham, V."

Now showing items 21-40 of 65

    • 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 ...

    • General Uniqueness Criteria for Ordinary Differential Equations 

      Lakshmikantham, V.; Samimi, Mansour (University of Texas at ArlingtonDepartment of Mathematics, 1982-02)
      **Please note that the full text is embargoed** ABSTRACT: This paper generalizes various uniqueness results and offers very general uniqueness criteria which include different types of results considered so far.

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

      Lakshmikantham, V.; Bernfeld, Stephen R. (University of Texas at ArlingtonDepartment of Mathematics, 1981-05)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...

    • 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 Principle for Differential Equations in Abstract Cones 

      Mitchell, Roger W.; Mitchell, A. Richard; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      **Please note that the full text is embargoed** ABSTRACT: Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result ...

    • 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 ...

    • Method of Quasi-Upper and Lower Solutions in Abstract Cones 

      Lakshmikantham, V.; Vatsala, A. S.; Leela, S. (University of Texas at ArlingtonDepartment of Mathematics, 1981-05)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...

    • The Method of Quasilinearization and Positivity of Solutions in Abstract Cones 

      Lakshmikantham, V.; Sety, Dolores D.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1976-03)
      **Please note that the full text is embargoed** ABSTRACT: The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the ...

    • The Method of Upper, Lower Solutions and Volterra Integral Equations 

      Ladde, G. S.; Pachpatte, B. G.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1980-12)
      **Please note that the full text is embargoed** ABSTRACT: In employing the method of upper and lower solutions to dynamical systems, one is required to impose a certain monotone property on the given system [5,6,11] When ...

    • Monotone Iterative Technique for Differential Equations in a Banach Space 

      Lakshmikantham, V.; Du, Sen-Wo (University of Texas at ArlingtonDepartment of Mathematics, 1981-02)
      **Please note that the full text is embargoed** ABSTRACT: 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]. ...

    • A Monotone Method for Infinite System of Nonlinear Boundary Value Problems 

      Lakshmikantham, V.; Chandra, Jagdish; Leela, S. (University of Texas at ArlingtonDepartment of Mathematics, 1976-08)
      **Please note that the full text is embargoed** ABSTRACT: Monotone iterative methods have been successfully used to generate improvable two-sided point-wise bounds on solutions of nonlinear boundary value problems for both ...

    • Monotone Method for Nonlinear Boundary Value Problems Arising in Transport Process 

      Pachpatte, B. G.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1981-04)
      **Please note that the full text is embargoed** ABSTRACT: Recently, monotone iterative methods have been successfully employed to prove existence of multiple solutions and point-wise bounds on solutions of nonlinear ...

    • Monotone Methods for Nonlinear Boundary Value Problems in Banach Spaces 

      Bernfeld, Stephen R.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1977-12)
      **Please note that the full text is embargoed** ABSTRACT: Monotone methods have been used to generate multiple solutions of nonlinear boundary value problems for both ordinary and partial differential equations. Keller ...

    • 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 ...

    • On a Measure of Nonconvexity and Applications 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      **Please note that the full text is embargoed** ABSTRACT: The measure of noncompactness which was introduced by Kuratowski [8] (in 1930) has now become an important tool in nonlinear analysis (although its value in that ...

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

      Lakshmikantham, V.; Deimling, K. (University of Texas at ArlingtonDepartment of Mathematics, 1978-06)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...

    • 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 ...

    • 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 ...

    • On the Construction of a Norm Associated with the Measure of Noncompactness 

      Bernfeld, Stephen R.; Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1976-02)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...

    • 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 ...