Multiplicity Of Positive Solutions To Integral Boundary Value Problem Of Second Order Impulsive Differential Equations

In this paper, we study the existence of multiple positive solutions for a class of integralboundary value problem for second order impulsive differential equations in Banach space. Themain result is obtained, proved by Avery-Peterson theorem and verifed with an example. Andwe consider an integral boundary value problem for second order impulsive integro-differentialequations in Banach space, which is more complicated, but the existence of multiple positivesolutions for the problem is also obtained and verifed. The investigation of the problems is ofhigh theoretical and practical signifcance.The contents of this paper are as follows:In chapter1,The background knowledge and development status of impulsive differentialequations with integral boundary value is prevented, the main work and subject sources arestated brivelyIn chapter2, Concepts of the cone, convex function, concave function are introduced, andthe Avery-Peterson theorem is given.In chapter3, The existence of the multiple positive solutions of a class integral boundaryvalue problem for second order impulsive differential equations is studied.In chapter4, we consider an integral boundary value problem for second order impulsiveintegro-differential equations in Banach space, which is more complicated than the problem inChapter three. The existence of multiple positive solutions for the problem is also obtained andverifed.