有序Banach空间二阶常微方程的非平凡周期解

Nontrivial periodic solutions to second order ordinary differential equations in ordered Banach spaces

讨论了有序Banach空间E中的非线性二阶微分方程-u″(t)+au(t)=f(t,u(t)),t∈R非平凡ω-周期解的存在性,其中a>0,f:R×E→E连续.在较一般的非紧性侧度条件与序条件下用凝聚映射的不动点指数理论获得了该问题非平凡ω-周期解的存在性与多重性结果。

The existence of nontrivial periodic solutions was discussed for nonlinear second order ordinary differential equations in an ordered Banach space E, -u（t） ＋ an（t） = f（t, u（t））, t ∈ R where a 〉 0 and f：R× E → E is continuous. Under more general conditions of noncompactness measure and semi-ordering, the existence and multiplicity results of nontrivial w-periodic solutions were obtained by employing the fixed point index theory of condensing mapping.