Nonlinear boundary value problem for first order impulsive integro-differential equations of mixed type (Q853960)

The paper deals with a class of integro-differential equations of mixed type, with added impulse. The authors study the nonlinear boundary value problem associated to this equation in a space of continuous differentiable functions. In the first part of the article, some comparison principles are stated and proved. They are used to obtain existence and uniqueness of solutions to the integro-differential equation, as well as lower and upper solutions. A monotone iterative technique is used in obtaining the existence of extremal solutions. The paper ends with some examples, that verifies the hypotheses of theorems.