Abstract:

In this paper, we discuss the existence of solutions for nonlinear boundary problem of first-order impulsive differential inclusions. In the presence of a lower solution α and an upper solution β in the reverse order β ≤ α, we establish the existence results by using Martelli's fixed point theorem with upper and lower solutions method. We find that if we give different definitions of lower and upper solutions in the reverse order, we can also get the existence results.

Key words: Impulsive differential inclusions, Nonlinear boundary conditions, Fixed point theorem, Lower and upper solutions in the reverse order