The existence and approximation of extremal solutions to several first-order discontinuous dynamic equations with nonlinear boundary value conditions

The goal of this paper is to give a general view of some different kinds of weak first-order discontinuous boundary value problems on an arbitrary time scale with nonlinear functional boundary value conditions.By assuming Carathéodory’s conditions and discontinuity, we prove the existence of extremal solutions for all the problems in the sector formed by a lower and an upper solution to the problem considered; moreover, the uniform approximation by a sequence of lower and upper solutions to the problem is guaranteed.