Impulsive coupled systems with generalized jump conditions

Abstract

This work considers a second-order impulsive coupled system with full nonlinearities, generalized impulse functions and mixed boundary conditions. This is the first time where such coupled systems are considered with nonlinearities with dependence on both unknown functions and their derivatives, together impulsive functions given by more general framework allowing jumps on the both functions and both derivatives. The arguments apply the fixed point theory, Green’s functions technique, L1 -Carathéodory functions theory and Schauder’s fixed point theorem. An application to the transverse vibration system of elastically coupled double-string is presented in the last section.