二阶微分方程周期边值问题解的存在性

On existence of solutions for PBVP of second order differential equations

为了进一步研究常微分方程周期边值问题解的存在性,利用上下解方法和拓扑度理论,构造两个新的比较定理,获得了二阶常微分方程周期边值问题解的两个存在性定理,此时仅要求f满足比单边Lipschitz条件更弱的条件,且不要求上下解满足常见的边界条件。对于上下解反向给定时,亦建立了相应的解的存在性定理。文中给出的数值表达式在形式上更简洁,更易验证,且条件更宽,改进了已有结果。

This paper presents an attempt to investigate the existence of solutions for periodic boundary value problems（PBVP） of ordinary differential equations,and introduces two existence theorems of solutions of the PBVP for second order differential equations are obtained by using the method of upper and lower solutions and the topological degree theory and establishing two new comparison theorem,where f satisfies some weaker conditions than the one-side Lipschitz condition and the lower and upper solutions need not satisfy the common boundary relations.Furthermore,the similar existence theorems are also obtained in the case when upper and lower solutions are in the reversed order.The paper features the mathematical expressions,simpler in form and easier to verify.The results improve the relative conclusions in the early times.