Impulsive problems on the half-line with infinite impulse moments

Abstract

We present a two-point impulsive boundary value problem on the half-line with infinite impulsive effects on the unknown function and its derivative given by generalized functions.

In this way, this problem can be applied to phenomena where the occurrence of infinite jumps depends not only on the instant, but also on their amplitude and frequency. The arguments apply Green’s functions and Schauder’s fixed-point theorem. The concept of equiconvergence at +∞ and at each impulsive moment is a key point to have a compact operator.