Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions

In this work we shall study the existence of extremal solutions for an impulsive problem with functional-boundary conditions and weak regularity assumptions, not only on the right-hand side of the equation and on the functions that define the boundary conditions, but also on the impulse functions, which will be required to be nondecreasing, but not continuous as well, as is customary in the literature. Moreover, in order to prove one of our results we shall study a general impulsive linear problem, giving a complete characterisation of resonance for it.