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

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