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摘要: 讨论了时间尺度上非线性二阶动力方程的特征值问题,该问题满足 m 点边界条件. 利用 Schauder 及 Krasnoselskii 不动点定理刻画了其特征值,给出了正解存在性结果. 还得到了特征值 λ 的具体的区间,使得在这些区间里 所讨论的边值问题至少 有一个正解存在.Abstract: The paper studied the eigenvalue problems for nonlinear second-order dynamic equations on time scales with m-point boundary conditions. Using Schauder'sand Krasnoselskii's fixed point theorems, the eigenvalues were characterized and the existence of positive solutions established. Several kinds of intervals ofλ were presented explicitly, in which the existence of at least one positive solution of BVP was guaranteed.
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