Browsing Department of Mathematics by Author "Vatsala, A. S."

Now showing items 1-12 of 12

    • Comparison Results for First and Second Order Boundary Value Problems at Resonance 

      Vatsala, A. S.; Shendge, G. R. (University of Texas at ArlingtonDepartment of Mathematics, 1982-05)
      **Please note that the full text is embargoed** ABSTRACT: It is well known that the comparison principle for the initial value problems has been very useful in the theory of differential equations [1, 2,5]. Recently, such ...

    • Comparison Results for Parabolic Differential Equations at Resonance 

      Vatsala, A. S.; Shendge, G. R. (University of Texas at ArlingtonDepartment of Mathematics, 1982-07)
      **Please note that the full text is embargoed** ABSTRACT: It is very well known that comparison principles for initial and boundary value problems for nonresonance cases have been very much used in the existence of solutions ...

    • 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 of Sobolev Type 

      Vaughn, Randy; Vatsala, A. S. (University of Texas at ArlingtonDepartment of Mathematics, 1978-12)
      **Please note that the full text is embargoed** ABSTRACT: Recently a new class of differential equations, called differential equations of Sobolev type was studied in [4] in which an existence theorem of Picards type ...

    • 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 Extremal Solutions and Comparison Results for Delay Differential Equations in Abstract Cones 

      Laughn, R. L.; Vatsala, A. S. (University of Texas at ArlingtonDepartment of Mathematics, 1979-10)
      **Please note that the full text is embargoed** ABSTRACT: The study of Cauchy problem for ordinary differential equations in a Banach space has been extensive [2,4,10]. It is of interest to look at the corresponding problem ...

    • 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 ...

    • Monotone Method for Equations Describing Transport Phenomena in a Banach Space 

      Vatsala, A. S.; Pachpatte, B. G. (University of Texas at ArlingtonDepartment of Mathematics, 1981-06)
      **Please note that the full text is embargoed** ABSTRACT: Existence of extremal solutions of initial and boundary value problems (B.V.P. for short) of differential equations in a Banach space has been recently considered ...

    • On the Existence of Periodic Quasi Solutions for First Order Systems 

      Vatsala, A. S. (University of Texas at ArlingtonDepartment of Mathematics, 1982-09)
      **Please note that the full text is embargoed** ABSTRACT: Recently the method of upper and lower solutions and Lyapunov-Schmitt method have been fruitfully employed to prove the existence of periodic solutions for scalar ...

    • Quasi-Solutions and Monotone Method for Systems of Nonlinear Boundary Value Problems 

      Vatsala, A. S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1980-02)
      **Please note that the full text is embargoed** ABSTRACT: In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for initial and boundary value problems of ordinary differential ...

    • Systems by the Method of Quasisolutions 

      Vatsala, A. S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1981-01)
      **Please note that the full text is embargoed** ABSTRACT: Recently [10] the method of lower and upper solutions has been extended to systems of reaction diffusion equations which has become very useful in dealing with ...