The Existence And Uniqueness Of Solutions For Several Classes Of Boundary Value Problems Of Semipositive Fractional Impulsive Differential Equations With P-Laplacian Operator

The objective of this dissertation is to study the existence and uniqueness of solutions to several kinds of boundary value problems of semi-positive fractional impulse differential equations with p-Laplacian operator.Equation boundary value problem,a class of semi-positive fractional impulse differential equations with p-Laplacian operator,including three-point boundary value problem and a class of semi-positive fractional impulse differential equations with p-Laplacian operator,four-point boundary value problem.Research,discuss the existence and uniqueness of its solution.Mainly use its equivalent integral equation,choose a suitable fixed point theory or upper and lower solution method to analyze it,and finally obtain sufficient conditions for the existence of the equation solution.The full text consists of five chapters.The content of the article is arranged as follows:The first chapter mainly describes the research background and research status of fractional differential equations,the basic knowledge of fractional calculus related to this paper,and the fixed point theory mainly used in this paper.In the second chapter,based on the existing boundary value problems of fractional impulse differential equations,a class of boundary value problems of semi-positive fractional impulse differential equations with p-Laplacian operator is discussed.First,the fractional impulse equations are analyzed,The integral equation equivalent to the solution of the equation is obtained.The properties of the integral equation are analyzed,mainly using the method of upper and lower solutions,combined with the Arzela-Ascoli theorem and Banach theorem,to obtain the existence and uniqueness of the positive solution of the boundary value problem,which is a sufficient condition that a positive solution of this equation exists and is unique.In the third chapter,the existence and uniqueness of the solutions of a class of three-point boundary value problems for semi-positive fractional impulse differential equations with p-Laplacian operator are studied.The analysis is carried out and the corresponding conditions are established,and the main result is a sufficient condition for the uniqueness and existence of the solution of the equation.The fourth chapter studies the existence of solutions to a class of four-point boundary value problems for a class of semi-positive fractional impulse differential equations with p-Laplacian operator.Using the Arzela-Ascoli theorem and the fixed point theorem,the core method is to solve the equation Transform to find the sufficient conditions for the existence of the solution of the boundary value problem.