Periodic solutions for generalized Liénard neutral equation with variable parameter (Q1004642)

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scientific article; zbMATH DE number 5527999
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Periodic solutions for generalized Liénard neutral equation with variable parameter
scientific article; zbMATH DE number 5527999

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    Periodic solutions for generalized Liénard neutral equation with variable parameter (English)
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    11 March 2009
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    Let \(\tau\) be a constant; \(\gamma, c\) be continuous periodic functions with period \(T>0;\) \(c\in C^2 (\mathbb{R},\mathbb{R})\) with \(|c(t)|\neq 1\) and \(c(t+T)=c(t).\) This paper deals with the investigation of a second-order neutral equation with variable parameter of the following form: \[ [x(t)-c(t)x(t-\tau)]''+f(x(t))x'(t)+g(x(t-\gamma(t)))=e(t), \] where \(f,g\in C(\mathbb{R},\mathbb{R}).\) Using Mawhin's continuation theorem, the authors establish the existence of periodic solutions to this equation.
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    neutral equation
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    periodic solution
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    Mawhin's continuation theorem
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    variable parameter
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