EXISTENCE OF SOLUTIONS FOR IMPULSIVE NONLINEAR DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

  • Selvaraj, B. (DEPT. OF MATH., KARUNYA UNIV.) ;
  • Arjunan, M. Mallika (DEPT. OF MATH., KARUNYA UNIV.) ;
  • Kavitha, V. (DEPT. OF MATH., KARUNYA UNIV.)
  • Received : 2009.07.07
  • Accepted : 2009.08.12
  • Published : 2009.09.25

Abstract

In this article, we study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive differential equation with nonlocal conditions u'(t) = Au(t) + f(t, u(t); Tu(t); Su(t)), $0{\leq}t{\leq}T_0$, $t{\neq}t_i$, u(0) + g(u) = $u_0$, ${\Delta}u(t_i)=I_i(u(t_i))$, i = 1,2,${\ldots}$p, 0<$t_1$<$t_2$<$\cdots$<$t_p$<$T_0$, in a Banach space X, where A is the infinitesimal generator of a $C_0$ semigroup, g constitutes a nonlocal conditions, and ${\Delta}u(t_i)=u(t_i^+)-u(t_i^-)$ represents an impulsive conditions.

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