Integral boundary value problems for first order nonlinear impulsive functional integro-differential differential equations

In this paper, we consider the existence of solutions for first order nonlinear impulsive functional integro-differential equations with integral boundary value conditions. We firstly build a new comparison theorem. Then by utilizing the monotone iterative technique and the method of lower and upper solutions, we obtain the existence of extremal solutions or quasi-solutions.     

On nonlinear two-point boundary value problems for impulsive differential-algebraic problems

In this paper, we investigate boundary value problems for first order impulsive differential-algebraic problems with causal operators. Note that a corresponding boundary condition is given by a nonlinear function. Using a monotone iterative method we formulate general sufficient conditions under which such problems have solutions (extremal or a unique). An example shows that corresponding assumptions are satisfied. The results are new.