Positive solutions of some nonlocal impulsive boundary value problem

TL;DR

This paper establishes new existence results for positive solutions of impulsive differential equations with nonlocal boundary conditions involving Stieltjes integrals, generalizing multi-point boundary conditions.

Contribution

It introduces novel existence theorems for positive solutions in impulsive differential equations with boundary conditions expressed via Stieltjes integrals, extending previous multi-point boundary condition studies.

Findings

Proved existence of positive solutions under new boundary conditions

Extended classical boundary conditions to include Stieltjes integral form

Generalized results to cover impulsive differential equations with nonlocal conditions

Abstract

We prove new results on the existence of positive solutions for some impulsive differential equation subject to nonlocal boundary conditions. Our boundary conditions involve an affine functional given by a Stieltjes integral. These cover the well known multi-point boundary conditions that are studied by various authors.