Results 51 to 60 of about 981 (105)
On the uniqueness of limit cycles for generalized Liénard systems
Open Mathematics, 2023 In this article, the general Liénard system dxdt=ϕ(y)−F(x),dydt=−g(x)\left\{\begin{array}{l}\frac{{\rm{d}}x}{{\rm{d}}t}=\phi (y)-F\left(x),\\ \frac{{\rm{d}}y}{{\rm{d}}t}=-g\left(x)\end{array}\right. is studied.
Zhou Hui, Yuan Yueding
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A Note on Homoclinic Orbits for Second Order Hamiltonian Systems [PDF]
, 2014 In this paper, we study the existence for the homoclinic orbits for the second order Hamiltonian systems. Under suitable conditions on the potential $V$, we apply the direct method of variations and the Fourier analysis to prove the existence of ...
Li, Bingyu +3 more
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Periodic solutions of some polynomial differential systems in dimension 5 via averaging theory
Nonautonomous Dynamical Systems, 2023 In this article, we provide sufficient conditions for the existence of periodic solutions for the polynomial differential system of the form x˙=−y+εP1(x,y,z,u,v)+h1(t),y˙=x+εP2(x,y,z,u,v)+h2(t),z˙=−u+εP3(x,y,z,u,v)+h3(t),u˙=z+εP4(x,y,z,u,v)+h4(t),v˙=λv ...
Tabet Achref Eddine, Makhlouf Amar
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, 2007 We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions.
Chen, Hongbin, Li, Yi
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Periodic solutions for nonautonomous second order Hamiltonian systems with sublinear nonlinearity
Boundary Value Problems, 2011 Some existence and multiplicity of periodic solutions are obtained for nonautonomous second order Hamiltonian systems with sublinear nonlinearity by using the least action principle and minimax methods in critical point theory.
Zhang Jihui, Wang Zhiyong
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Advanced Nonlinear Studies, 2019 Efficient conditions guaranteeing the existence and multiplicity of T-periodic solutions to the second order differential equation u′′=h(t)g(u){u^{\prime\prime}=h(t)g(u)} are established.
Hakl Robert, Zamora Manuel
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Limit cycles of Liénard polynomial systems type by averaging method
Moroccan Journal of Pure and Applied Analysis, 2020 We apply the averaging theory of first and second order for studying the limit cycles of generalized polynomial Linard systems of the ...
Boulfoul Amel, Mellahi Nawal
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On the limit cycles for a class of eighth-order differential equations
Moroccan Journal of Pure and Applied Analysis, 2020 In this article, we provide sufficient conditions for the existence of periodic solutions of the eighth-order differential equation x(8)-(1+p2+λ2+μ2)x(6)+Ax⃜+Bx¨+p2λ2μ2x=ɛF(t,x,x˙,x¨,x⃛,x⃜,x(5),x(6)x(7)),{x^{\left( 8 \right)}} - \left( {1 + {p^2 ...
Berrehail Chems Eddine +2 more
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, 2013 We present a geometric characterization of the nonlinear smooth functions $V: R\to R$ for which the origin is a global isochronous center for the scalar equation $\ddot x=-V'(x)$.
Gorni, Gianluca, Zampieri, Gaetano
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Periodic or homoclinic orbit bifurcated from a heteroclinic loop for high-dimensional systems
Open MathematicsConsider an autonomous ordinary differential equation in Rn{{\mathbb{R}}}^{n}, which has a heteroclinic loop. Assume that the heteroclinic loop consists of two degenerate heteroclinic orbits γ1{\gamma }_{1}, γ2{\gamma }_{2} and two saddle points with ...
Long Bin, Yang Yiying
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