【摘要】 应用Leggett-Williams不动点定理及其推论研究二阶微分方程周边值问题,并在较有关文献更弱的条件下分别证明了其至少有三个或至少有两个正解的存在性结果.使用相同的理论方法讨论了一类2n阶微分方程周期边值问题,同样获得了其至少有三个或至少有两个正解的存在性定理.论文所得结论在一定程度上推广和改进了所引用相关文献中的一些结果.更多还原

【Abstract】 In the first place,we investigate in this article the periodic boundary value problems for second-order differential equations by an application of Leggett-Williams’ Fixed Point Theorem and its corollary,and prove under much weaker conditions than those used in the cited literature the existence results of at least three or at least two positive solutions to the problems studied,respectively.Secondly,we utilize the same theoretical approaches to discuss a family of periodic boundary value problems for 2nth-order differential equations and obtain the similar existence theorems on their possessing at least three or at least two positive solutions.At last,we should point out that all the results gained here generalize and develop to some extent those ones in the relevant literature cited herein.更多还原