Study on the Multi-Point Boundary Value Problem for Second-Order Nonlinear Impulsive Integro-Differential Equation

• Published in: Journal of mathematics (Hidawi) Vol. 2023; pp. 1 - 16
• Main Authors: Li, Haiyan, Guo, Yuheng
• Format: Journal Article
• Language: English
• Published: Cairo Hindawi 2023; Hindawi Limited
• Subjects: Banach spaces; Biological control; Boundary value problems; Differential equations; Dynamical systems; Existence theorems; Fixed points (mathematics); Infectious diseases; Mathematics; Operators (mathematics); Typhoid
• ISSN: 2314-4629; 2314-4785
• DOI: 10.1155/2023/3120723

In the field of biological control, there are a large number of systems that gradually evolve over a certain period of time. However, due to some natural or human intervention behavior, the system state will be subjected to some relatively short time interference, so that the system state changes in an instant. This sudden change of state makes the system not simply described by continuous or discrete dynamical systems, but by means of impulse dynamical systems. In this paper, the multi-point boundary value problem of a class of second-order nonlinear impulsive integral differential equations is studied on the basis of impulsive differential equation theory. The main results of this kind of equation are obtained by using the fixed point theorem of strict set contraction operator. Under certain assumptions, the existence of the solution of the equation is proved by constructing the operator on the special cone. Finally, combined with the practical application, the theory was applied to the stability prediction of biological ecosystem, and the correctness of the conclusion was verified.