The Existence Of Solutions For Several Kinds Of Nonlinear Impulsive Differential Equations

Nonlinear functional analysis is a research field of mathematics which has profound theories and extensive applications. It takes the nonlinear problems appearing in math-ematics and the natural sciences as background to establish some general theories and methods to handle nonlinear problems. In recent years, nonlinear differential equation-s have received highly attention of the domestic and foreign mathematics and natural scicience field,and become one of the hottese issues in the international research field. Im-pulsive differential equations have been widely used in chemical, engineering, population dynamics and economics, etc. By using nonlinear analysis tools, many mathematicians obtained existence results and qualitative properties of solutions for nonlinear impulsive differential equations.We mainly stuudy the existence of solutions for several nonlinear impulsive differential equations. The paper is organized as follows:In Chapter 1, we are concerned with the impulsive fractional integro-differential e-quation with anti-periodic boundary condition and constant coefficient.The existence and uniqueness results are established by the Banach contraction mapping principle and the Krasnoselskii's fixed point theorems.In Chapter 2, we investigate the impulsive fractional q-difference equations with anti-periodic conditions By using the theorem of nonlinear alternative of Leray-Schauder type and the Banach contraction mapping principle, we prove the existence and uniqueness results of solutions.In Chapter 3, we study the second order impulsive differential system with integral boundary conditions The paper employs the Krasnoselskii's theorem in double cones to investigate the existence of at least two nonnegative solutions for boundary value problem with sign-changing nonlinearity.