Improved Nth order averaging theory for periodic systems
نویسندگان
چکیده
منابع مشابه
ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *
The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.
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For ε ≠ 0 sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x'' + f (x) x' + n2x + g (x) = ε2p1 (t) + ε3 p2(t), where n is a positive integer, f : ℝ → ℝ is a C 3 function, g : ℝ → ℝ is a C 4 function, and p i : ℝ → ℝ for i = 1, 2 are continuous 2π-periodic function. The main tool used in this paper...
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In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(t) = f(t, u(t));u(a) − u(b) = λi ∈ R; i = 0, ..., n− 1. Where f is a Carathéodory function. We obtain sufficient conditions in f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n ≥ 3 either α ≤ β or α ≥ β. For this, we study...
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In this paper, by using an initial value problem method and a global inverse function theorem, we give some existence and uniqueness results of periodic solution for a class of nth-order nonlinear ordinary differential equations. AMS (MOS) Subject Classification. 34B10, 34B15, 34L16, 65L05, 65L10
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and Applied Analysis 3 Now, let f̃ : R 1 → R be a continuous function, T -periodic with respect to the first variable, and consider the nth-order differential equation u n f̃ ( t, u, u′, u′′, . . . , u n−1 ) . 2.5 Lemma 2.1 see 14 . Assume that the following conditions hold. i There exists ρ > 0 such that, for each λ ∈ 0, 1 , one has that any possible T -periodic solution u of the problem u n λf̃ ...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1990
ISSN: 0022-0396
DOI: 10.1016/0022-0396(90)90083-2