Periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argument
نویسندگان
چکیده
منابع مشابه
Periodic solutions for prescribed mean curvature Rayleigh equation with a deviating argument
where τ , e ∈ C(R,R) are T-periodic, and f , g ∈ C(R × R,R) are T-periodic in the first argument, T > is a constant. In recent years, there are many results on the existence of periodic solutions for various types of delay differential equation with deviating arguments, especially for the Liénard equation and Rayleigh equation (see [–]). Now as the prescribed mean curvature ( x ′(t) √ +x′...
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In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of T -periodic solutions for a kind of Rayleigh equation with a deviating argument of the form x′′ + f(x′(t)) + g(t, x(t− τ(t))) = p(t).
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where g(t,x(t)) may be unbounded as x → 0+. Equation (1.1) is of repulsive type (resp. attractive type) if g(t,x(t))→ –∞ (resp. g(t,x(t))→ +∞) as x→ 0+. Using Mawhin’s continuation theorem, the author proved that Eq. (1.1) has at least one T-periodic solution. Zhang’s work has attracted much attention of many specialists in differential equations. In 2014,Wang [2] investigated the existence of ...
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In this work, we use the coincidence degree theory to establish new results on the existence and uniqueness of T -periodic solutions for a kind of Liénard equation with a deviating argument of the form x (t)+ f (x(t))x (t)+ g(t, x(t − τ(t))) = p(t). c © 2007 Elsevier Ltd. All rights reserved.
متن کاملPeriodic Solutions for p-Laplacian Liénard Equation with a Deviating Argument
By employing Mawhin’s continuation theorem, the existence of periodic solutions of the p-Laplacian Liénard equation with a deviating argument (φp(x′(t)))′ + f(x(t))x′(t) + g(x(t− τ(t))) = e(t) under various assumptions are obtained. Keywords—periodic solution, Mawhin’s continuation theorem, deviating argument.
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2013
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2013-88