The Existence Of Positive Solutions For Boundary Value Problems Of Two Types Of Difference Equations

In real life,due to the further development of disciplines such as medicine,biomathematics,economics,and modern physics and chemistry,many scholars have proposed many mathematical models described by difference equations.For example,the calculation of compound interest,the determination of the amount of repayment,the growth of the economy and the assessment of benefits,the recurrence of probability in random phenomena,and the description of changes in the number of populations.The difference equation provides a very suitable mathematical model for the researcher's development process such as the above-mentioned practical problems.Therefore,the existence of positive solutions for the boundary value problems of difference equations has attracted widespread attention.Many scholars used the fixed point index to study the existence of positive solutions to the boundary value problems of differential equations,and used the Krasnosel's fixed point theorem to study the existence of positive solutions to the boundary value problems of fourth-order difference equations.Through the results of people's research before reading,this paper will study the following boundary value problems:1)The existence of positive solutions of the boundary value problem for third-order difference equation;2)The existence of positive solutions of the boundary value problem for fourth-order difference equation;3)The existence of positive solutions of the boundary value problem for fourth-order difference system;In order to solve the above problems,this paper first finds the Green's function of the boundary value problem,and then defines the appropriate Banach space,cones,and norm,and gives the appropriate operator.The existence of positive solutions of two types of boundary value problems is studied by means of fixed point exponential theorem and Krasnosel's fixed point theorem.