Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 105, pp. 1-14.

Title: Existence and uniqueness of solutions to first-order systems of
       nonlinear impulsive boundary-value problems with sub-, super-linear 
       or linear growth

Authors: Juan J. Nieto (Univ. de Santiago de Compostela, Spain)
         Christopher C. Tisdell (Univ. of New South Wales, Australia)

Abstract:
 In this work we present some new results concerning the existence and
 uniqueness of solutions to an impulsive first-order, nonlinear ordinary
 differential equation with "non-periodic" boundary conditions. These
 boundary conditions include, as a special case, so-called 
 "anti-periodic" boundary conditions.
 Our methods to prove the existence and uniqueness of
 solutions involve new differential inequalities,
 the classical fixed-point theorem of Schaefer,
 and the Nonlinear Alternative.
 Our new results apply to systems of impulsive differential
 equations where the right-hand side of the equation may grow
 linearly, or sub- or super-linearly in its second argument.

Submitted March 14, 2007. Published July 30, 2007.
Math Subject Classifications: 34A37, 34B15.
Key Words: Existence and uniqueness of solutions; boundary value  problems;
           impulsive equations; fixed-point theory; system of equations.