A class of BVPS for first order impulsive integro-differential equations

作者：Liang, Jitai; Liu, Yiliang^*; Liu, Zhenhai

来源：Applied Mathematics and Computation, 2011, 218(7): 3667-3672.

DOI：10.1016/j.amc.2011.09.009

• Impulsive integro-differential equation
• Upper and lower solutions
• Monotone iterative technique

In this paper, we study the impulsive integro-differential equations
{u'(t) = f(t, u(t), Tu, Su), t not equal t(k), t is an element of J = [0, 1],
Delta u(t(k)) = I(k)(u(t(k))), k = 1, 2, ... , m,
u(0) = au(1) + bu(xi).
The existence of maximal and minimal solutions to the problem is proved by using an upper and lower solutions method together with monotone iterative technique. And two monotone sequences which uniformly converge to the relevant solutions are obtained. An example is included to show the applicability of our results.

• 出版日期2011-12-1
• 单位广西民族大学