Abstract This work contains a general theory for coupled systems, with regular and singular semi-linear fully differential equations of higher order, with the possibility of equations of different order and generalized impulsive effects, depending on both variables and some derivatives. Two types of results are shown: first, an existence theorem, proved via fixed point theory. Secondly, we define a new type of coupled lower and upper solutions, and sufficient conditions to get the localization of a solution and some of its derivatives. The method is based on considering an auxiliary, truncated, and perturbated problem, whose solutions are also solutions of the initial problem. An application to the flexural vibration of a single-span suspension bridge is presented for the regular case, and an example for singular Laplacians.
Minhós et al. (Thu,) studied this question.