Infinite Solutions Of Impulsive Differential Equations Under Non-symmetrical Perturbation

Impulsive differential equations is the important branch of differential equations developed in the middle of the last century.It has important applications in many fields,such as control systems,information science,aerospace technology,communications,and life sciences.The most prominent feature of the impulsive differential system is that it fully consider the influence of transient mutation on the state,and can more accurately reflect change trend.Its qualitative theory has received extensive attention from scholars.This paper mainly study the infinite multiplicity of impulsive equations under non-symmetrical perturbations by using the variational method and perturbation technique.The existence of the solution of the impulse boundary value problem is transformed into the existence of the critical point of the functional in the function space.The first chapter of the article briefly describes the background and development of impulsive differential equations,and introduces the main theorems needed in this paper.In the second chapter,we discuss a class of high-order impulsive differential equations under non-symmetrical perturbations,and obtain sufficient conditions for the existence of infinite solutions.In the third chapter,the boundary value problems of second-order impulsive equations under non-symmetrical perturbations are discussed.The conditions guaranteeing existence of infinite high-energy solutions and infinitely small solutions are obtained.