Dynamic Systems and Applications 20 (2011) 307-316 NONLINEAR FIRST-ORDER SEMIPOSITONE PROBLEMS OF IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES

The theory of impulsive differential equations is emerging as an important area of investigation, since it is a lot richer than the corresponding theory of differential equations without impulse effects. Moreover, such equations may exhibit several real world phenomena in physics, biology, engineering, etc. (see [3, 4, 20]). At the same time, the boundary value problems for impulsive differential equations and impulsive difference equations have received much attention [2, 10, 17, 18, 21–23, 25–28, 30, 32]. On the other hand, recently, the theory of dynamic equations on time scales has become a new important branch (see, for example, [1, 6, 7, 16, 19]). Naturally, some authors have focused their attention on the boundary value problems of impulsive dynamic equations on time scales [5, 8, 9, 12–15, 24, 33]. However, to the best of our knowledge, few papers concerning PBVPs of impulsive dynamic equations on time scales with semi-position condition.