Browsing by Author "Lakshmikantham, V."

Now showing items 1-20 of 65

    • 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 ...

    • Comparison Results for Reaction-Diffusion Equations in a Banach Space 

      Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1979-06)
      **Please note that the full text is embargoed** ABSTRACT: Let T be the temperature and n the concentration of a combustible substance. A simple model governing the combustion of the material is given by [see pdf for ...

    • Competitive-Cooperative Processes and Stability of Diffusion Systems 

      Lakshmikantham, V.; Ladde, G. S. (University of Texas at ArlingtonDepartment of Mathematics, 1978)
      **Please note that the full text is embargoed** ABSTRACT: Very recently, the stability analysis of deterministic [12], random [12,13] competitive-cooperative process has been made in a systematic and unified way. It is ...

    • 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 ...

    • 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 ...

    • Differential Inequalities and Flow-Invariance via Linear Functionals 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1977-05)
      **Please note that the full text is embargoed** ABSTRACT: This paper deals with flow-invariance properties with respect to [see pdf for notation] and resulting comparison inequalities. Both the order relation He and the ...

    • Equations with Unbounded Delay: a Survey 

      Lakshmikantham, V.; Corduneanu, C. (University of Texas at ArlingtonDepartment of Mathematics, 1979-08)
      **Please note that the full text is embargoed** ABSTRACT: The theory of equations with delay has been considerably developed during the past 30 years. The first book dedicated to this subject has been published by A. D. ...

    • Existence and Asymptotic Behavior of Reaction-Diffusion Systems Via Coupled Quasi-Solutions 

      Ladde, G. S.; Vatsala, A. S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1980-08)
      **Please note that the full text is embargoed** ABSTRACT: In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for differential systems a property called quasimonotone ...

    • Existence and Comparison Results for a Class of Volterra Integral Equations of Sobolev Type 

      Vatsala, A. S.; Lakshmikantham, V.; Vaughn, Randy (University of Texas at ArlingtonDepartment of Mathematics, 1978-09)
      **Please note that the full text is embargoed** ABSTRACT: Recently [2] a class of new differential equations called Sobolev type differential equations was introduced and Picard type existence theorem for such equations ...

    • 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 ...

    • Existence and Comparison Theorems for Differential Equations in Banach Spaces 

      Lakshmikantham, V.; Deimling, K. (University of Texas at ArlingtonDepartment of Mathematics, 1978-07)
      **Please note that the full text is embargoed** ABSTRACT: In our recent paper [3] we have studied the existence of maximal and minimal solutions to the IVP in a Banach space [see pdf for notation]. (1) [see pdf for ...

    • 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 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) ...

    • Existence of Coupled Quasi-solutions of Systems of Nonlinear Elliptic Boundart Value Problems 

      Lakshmikantham, V.; Ladde, G. S.; Vatsala, A. S. (University of Texas at ArlingtonDepartment of Mathematics, 1983-06)
      **Please note that the full text is embargoed** ABSTRACT: Systems of nonlinear elliptic boundary value problems arise in many applications such as multiple chemical reactions that take place in an isothermal or nonisothermal ...

    • Existence of Coupled Quasi-solutions of Systems of Nonlinear Reaction-diffusion Equations 

      Lakshmikantham, V.; Ladde, G. S. (University of Texas at ArlingtonDepartment of Mathematics, 1983-10)
      **Please note that the full text is embargoed** ABSTRACT: Systems of nonlinear parabolic initial boundary value problems arise in many applications such as epidemies, ecology, biochemistry, biology, chemical and nuclear ...

    • Existence of Periodic Solutions of Nonlinear Boundary Value Problems and the Method of Upper and Lower Solutions 

      Lakshmikantham, V.; Kannan, R. (University of Texas at Arlington, 1981-11)
      **Please note that the full text is embargoed** ABSTRACT: We study the existence of periodic solutions of second order nonlinear differential equations by combining the method of upper and lower solutions and the method ...

    • Existence of Periodic Solutions of Semilinear Parabolic Equations and the Method of Upper and Lower Solutions 

      Lakshmikantham, V.; Kannan, R. (University of Texas at ArlingtonDepartment of Mathematics, 1982-04)
      **Please note that the full text is embargoed** ABSTRACT: The existence of periodic solutions of semilinear parabolic equations has been investigated by several authors [1-10,15-18] by different methods such as the method ...

    • Fixed Point Theorems for PPF Mappings Satisfying Inwardness Conditions 

      Bernfeld, Stephen R.; Reddy, Y. M.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1980-07)
      **Please note that the full text is embargoed** ABSTRACT: In this paper we continue our recent development [1] of the theory of fixed point theorems of nonlinear operators whose domain and range are different Banach spaces. ...

    • Fixed Point Theorems on Closed Sets Through Abstract Cones 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1976-03)
      **Please note that the full text is embargoed** ABSTRACT: Let D be a closed subset of a complete metric space (X,p). We seek (i) conditions upon which a map T : D -> X has a fixed point in D and (ii) the construction of ...