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Về một lớp phương trình Volterra tích phân vi diệt trễ
Tóm tắt
Trong bài báo này, chúng tôi xem xét lớp phương trình Volterra tích phân vi diệt trễ sau đây trong không gian Banach $$\begin{aligned} \dot{x}\left( t\right) =Ax\left( t\right) +\int _{0}^{t}a\left( t-\tau \right) \mathcal {F}x\left( \tau \right) d\tau +\int _{0}^{t}b\left( t-\tau \right) Lx_{\tau }d\tau , \end{aligned}$$ trong đó tham số trễ $$Lx_{\tau }$$ của phương trình này được đưa vào tích phân như một tích chập với hạt nhân vô hướng. Bằng cách sử dụng lý thuyết các nhóm bán, chúng tôi thiết lập tính khả thi tốt của bài toán đã xem xét bằng cách sử dụng nhiễu loạn Miyadera–Voigt và cũng nghiên cứu phân tích phổ của một bài toán Cauchy trừu tượng liên quan.
Từ khóa
#phương trình vi diệt #phương trình Volterra #không gian Banach #lý thuyết nhóm bán #phân tích phổTài liệu tham khảo
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