Balachandran Krishnan

Publications (8)0 Total impact

• Source

  Available from: txstate.edu

  Article: Existence of solutions for quasilinear delay integrodifferential equations with nonlocal conditions

  Balachandran Krishnan, Francis Paul Samuel
  [show abstract] [hide abstract]
  ABSTRACT: We prove the existence and uniqueness of mild and classical solution to a quasilinear delay integrodifferential equation with nonlocal condition. The results are obtained by using $C_0$-semigroup and the Banach fixed point theorem.
  Electronic Journal of Differential Equations. 01/2009;
• Source

  Available from: sanu.ac.rs

  Article: On solutions of a Volterra integral equation with deviating arguments

  M. Diana Julie, Balachandran Krishnan
  [show abstract] [hide abstract]
  ABSTRACT: In this article, we establish the existence and asymptotic characterization of solutions to a nonlinear Volterra integral equation with deviating arguments. Our proof is based on measure of noncompactness and the Schauder fixed point theorem.
  Electronic Journal of Differential Equations. 01/2009;
• Source

  Available from: tcd.ie

  Article: Existence of mild solutions for quasilinear integrodifferential equations with impulsive conditions

  Balachandran Krishnan, Francis Paul Samuel
  [show abstract] [hide abstract]
  ABSTRACT: We prove the existence and uniqueness of mild solutions of quasilinear integrodifferential equations with nonlocal and impulsive conditions in Banach spaces. The results are obtained by using a fixed point technique and semigroup theory. Examples are provided to illustrate the theory.
  Electronic Journal of Differential Equations. 01/2009;
• Source

  Available from: nsc.ru

  Article: Asymptotic behavior of solutions to functional integral equation with deviating arguments

  M. Diana Julie, Balachandran Krishnan
  [show abstract] [hide abstract]
  ABSTRACT: This article presents results on the existence and asymptotic behavior of solutions of a functional integral equation with deviating arguments. The proof of our main result uses the classical Schauder fixed point theorem and the technique of measures of noncompactness.
  Electronic Journal of Differential Equations. 01/2008;
• Source

  Available from: nsc.ru

  Article: Approximate controllability of neutral stochastic integrodifferential systems in Hilbert spaces

  Subalakshmi Ravikumar, Balachandran Krishnan
  [show abstract] [hide abstract]
  ABSTRACT: In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory.
  Electronic Journal of Differential Equations. 01/2008;
• Source

  Available from: preprints.org

  Article: Regularity of solutions of Sobolev type semilinear integrodifferential equations in Banach spaces

  Balachandran Krishnan, Karunanithi Subbarayan
  [show abstract] [hide abstract]
  ABSTRACT: In this article, we prove the existence of mild and classical solutions of Sobolev type semilinear integrodifferential equations of the form $$ frac{d}{dt}[Ex(t)] = A[x(t)+int_0^tF(t-s)x(s)ds]+f(t,x(t)) $$ in Banach spaces. The results are obtained by using the Banach contraction mapping principle and resolvent operator. An application is provided to illustrate the theory.
  Electronic Journal of Differential Equations. 01/2003;
• Source

  Available from: hindawi.com

  Article: On a Volterra integral equation with deviating arguments

  Balachandran Krishnan
  [show abstract] [hide abstract]
  ABSTRACT: We prove an existence theorem for nonlinear Volterra integral equation with deviating arguments without assuming the Lipschitz condition.
  Journal of Applied Mathematics and Stochastic Analysis. 01/1990;
• Article: An existence theorem for nonlinear delay differential equations

  Balachandran Krishnan
  [show abstract] [hide abstract]
  ABSTRACT: In this paper we prove a theorem on the existence of solutions of nonlinear delay differential equations, with implicit derivatives. The result is established using the measure of noncompactness of a set and Darbo's fixed point theorem.
  Journal of Applied Mathematics and Stochastic Analysis. 01/1989;