Browsing Department of Mathematics by Author "Leela, S."

Now showing items 1-15 of 15

    • Cone-Valued Lyapunov Functions 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1976-08)
      **Please note that the full text is embargoed** ABSTRACT: It is very well known that employing a single Lyapunov function and the theory of scalar differential inequality offers a useful mechanism to study a ...

    • Existence and Monotone Method for Periodic Solutions of First Order Differential Equations 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1981-09)
      **Please note that the full text is embargoed** ABSTRACT: An attempt was made recently in [3] to combine fruitfully the two basic techniques, namely the method of upper and lower solutions and the Lyapunov-Schmitt method ...

    • Existence and Uniqueness of Solutions of Delay Differential Equations on a Closed Subset of a Banach Space 

      Moauro, V.; Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1977-05)
      **Please note that the full text is embargoed** ABSTRACT: In an earlier work [5], sufficient conditions for the existence of solutions in a closed subset F of a Banach space E for the Cauchy problem (1.1) [see pdf for ...

    • Existence of Solutions in a Closed Set for Delay Differential Equations in Banach Spaces 

      Moauro, V.; Leela, S. (University of Texas at ArlingtonDepartment of Mathematics, 1977-01)
      **Please note that the full text is embargoed** ABSTRACT: The study of the Cauchy problem for ordinary differential equations in a Banach space has been extensive [1,3-7,9-12]. The two main directions that are followed ...

    • 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 ...

    • 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 Second Order Periodic Boundary Value Problems 

      Leela, S. (University of Texas at ArlingtonDepartment of Mathematics, 1982-07)
      **Please note that the full text is embargoed** ABSTRACT: In recent years, there has been an extensive study of the existence of periodic solutions [1,8-11,14,15]. In, [8,11], the existence of solutions of first and second ...

    • Monotone Technique for Periodic Solutions of Differential Equations 

      Leela, S. (University of Texas at ArlingtonDepartment of Mathematics, 1982-07)
      **Please note that the full text is embargoed** ABSTRACT: The existence of periodic solutions has received a great deal of attention in recent years [1,7-11,14]. In [8,11] the existence of solutions of first and ...

    • 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 Existence of Zeros of Lyapunov-Monotone Operators 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1975-02)
      **Please note that the full text is embargoed** ABSTRACT: Consider a nonlinear operator T from a Banach space into itself. The study of the existence of zeros of T plays an important role in yielding fixed points of ...

    • On the Method of Upper and Lower Solutions in Abstract Cones 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1981-02)
      **Please note that the full text is embargoed**

    • Quasi-Solutions, Vector Lyapunov Functions and Monotone Method 

      Leela, S.; Lakshmikantham, V.; Oguztoreli, M. N. (University of Texas at ArlingtonDepartment of Mathematics, 1980-02)
      **Please note that the full text is embargoed** ABSTRACT: It is now well known that the method of vector Lyapunov functions provides an effective tool to investigate the properties of large scale interconnected dynamical ...

    • Stability of Differential Systems with Impulsive Perturbations in Terms of Two Measures 

      Leela, S. (University of Texas at ArlingtonDepartment of Mathematics, 1977-01)
      **Please note that the full text is embargoed** ABSTRACT: The study of differential systems of the form (1.1) [see pdf for notation] where [see pdf for notation] denotes the distributional derivative of [see pdf for ...

    • 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 ...

    • A Technique in Stability Theory of Delay-Differential Equations 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1978-04)
      **Please note that the full text is embargoed** ABSTRACT: In the study of stability theory for delay-differential equations using Lyapunov functions and the theory of differential inequalities, it becomes necessary to ...