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Giải pháp tuần hoàn cho một lớp hệ phương trình vi phân trễ bậc hai
Tóm tắt
Xem xét bài toán giá trị biên định kỳ
$$\left \{ \textstyle\begin{array}{ll} \ddot{u}(t)+r u(t-\tau)+\nabla F(t, u(t-\tau))=0, \quad\mbox{a.e. } t\in [0,2\tau],\\ u(0)-u(2\tau)=\dot{u}(0)-\dot{u}(2\tau)=0, \end{array}\displaystyle \right . $$
Trong đó
$\tau>0$ là một hằng số cho trước,
r\in\mathbf{R} là một tham số. Các giải pháp tuần hoàn được thu được bằng cách sử dụng các định lý liên kết.
Từ khóa
#phương trình vi phân #giải pháp tuần hoàn #hệ phương trình trễ #định lý liên kếtTài liệu tham khảo
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