Periodic Solutions for Nonlinear Differential Equation with Functional Delay
Keyword(s):
Abstract We use the modification of Krasnoselskii's fixed point theorem due to T. A. Burton ([Proc. Amer. Math. Soc. 124: 2383–2390, 1996]) to show that the scalar nonlinear differential equation with functional delay 𝑥′(𝑡) = –𝑎(𝑡)𝑥3(𝑡) + 𝐺(𝑡, 𝑥3(𝑡 – 𝑟(𝑡))) has a periodic solution. It is not required that 𝑟(𝑡) be differentiable, while 𝑎 and 𝐺 are continuous with respect to their arguments.
2006 ◽
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pp. 175-182
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