Báo Cáo Báo cáo hóa học FIRST- AND SECOND-ORDER DYNAMIC EQUATIONS WITH IMPULSE

FIRST- AND SECOND-ORDER DYNAMIC EQUATIONS WITH IMPULSE F. M. ATICI AND D. C. BILES Received 3 December 2004 and in revised form 11 February 2005

We present existence results for discontinuous first- and continuous second-order dynamic equations on a time scale subject to fixed-time impulses and nonlinear boundary conditions.

1. Introduction

We first briefly survey the recent results for existence of solutions to first-order problems with fixed-time impulses. Periodic boundary conditions using upper and lower solutions were considered in [19], using degree theory. A nonlinear alternative of Leray-Schauder type was used in [15] for initial conditions or periodic boundary conditions. The monotone iterative technique was employed in [14] for antiperiodic and nonlinear boundary conditions. Lower and upper solutions and periodic boundary conditions were studied in [20]. Semilinear damped initial value problems in a Banach space using fixed point theory were investigated in [6].