scholarly journals Harmonic and subharmonic solutions of quadratic Liénard type systems with sublinearity

2021 ◽  
Vol 6 (11) ◽  
pp. 12913-12928
Author(s):  
Chunmei Song ◽  
◽  
Qihuai Liu ◽  
Guirong Jiang ◽  
Keyword(s):  
Differential Equations ◽  
Type Systems ◽  
Second Order ◽  
Subharmonic Solutions ◽  
Twist Theorem

<abstract><p>In this paper, we prove the existence of harmonic solutions and infinitely many subharmonic solutions of dissipative second order sublinear differential equations named quadratic Liénard type systems. The method of the proof is based on the Poincaré-Birkhoff twist theorem.</p></abstract>

One-Signed Harmonic Solutions and Sign-Changing Subharmonic Solutions to Scalar Second Order Differential Equations

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Alberto Boscaggin
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Point Theorem ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions

AbstractUsing a recent modified version of the Poincaré-Birkhoff fixed point theorem [19], we study the existence of one-signed T-periodic solutions and sign-changing subharmonic solutions to the second order scalar ODEu′′ + f (t, u) = 0,being f : ℝ × ℝ → ℝ a continuous function T-periodic in the first variable and such that f (t, 0) ≡ 0. Partial extensions of the results to a general planar Hamiltonian systems are given, as well.

Subharmonic solutions with prescribed minimal period for some second-order impulsive differential equations

2012 ◽  
Vol 75 (4) ◽  
pp. 2249-2255 ◽  
Author(s):  
Zhiguo Luo ◽  
Jing Xiao ◽  
Yanli Xu
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Minimal Period ◽  
Subharmonic Solutions

Subharmonic solutions to second-order differential equations with periodic nonlinearities

2000 ◽  
Vol 41 (5-6) ◽  
pp. 649-667 ◽  
Author(s):  
Enrico Serra ◽  
Massimo Tarallo ◽  
Susanna Terracini
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions

scholarly journals The Integrating Factors for Riccati and Abel Differential Equations

2015 ◽  
Vol 7 (2) ◽  
pp. 125
Author(s):  
Chein-Shan Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Type Systems ◽  
Second Order ◽  
Numerical Schemes ◽  
Riccati Differential Equation ◽  
Group Preserving Scheme ◽  
Abel Differential Equation ◽  
Abel Differential Equations

We can recast the Riccati and Abel differential equationsinto new forms in terms of introduced integrating factors.Therefore, the Lie-type systems endowing with transformation Lie-groups$SL(2,{\mathbb R})$ can be obtained.The solution of second-order linearhomogeneous differential equation is an integrating factorof the corresponding Riccati differential equation.The numerical schemes which are developed to fulfil the Lie-group property have better accuracy and stability than other schemes.We demonstrate that upon applying the group-preserving scheme (GPS) to the logistic differential equation, it is not only qualitatively correct for all values of time stepsize $h$, and is also the most accurate one among all numerical schemes compared in this paper.The group-preserving schemes derived for the Riccati differential equation, second-order linear homogeneous and non-homogeneous differential equations, the Abel differential equation and higher-order nonlinear differential equations all have accuracy better than $O(h^2)$.

Subharmonic Solutions for Some Second-Order Differential Equations with Singularities

1993 ◽  
Vol 24 (5) ◽  
pp. 1294-1311 ◽  
Author(s):  
Alessandro Fonda ◽  
Raúl Manásevich ◽  
Fabio Zanolin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions

scholarly journals Subharmonic solutions for second order differential equations

1993 ◽  
Vol 1 (1) ◽  
pp. 49 ◽  
Author(s):  
Alessandro Fonda ◽  
Miguel Ramos ◽  
Michael Willem
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions

scholarly journals Subharmonic Solutions of Nonautonomous Second Order Differential Equations with Singular Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
N. Daoudi-Merzagui ◽  
F. Derrab ◽  
A. Boucherif
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Saddle Point ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Second Order ◽  
Saddle Point Theorem ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions ◽  
Singular Nonlinearities

We discuss the existence of subharmonic solutions for nonautonomous second order differential equations with singular nonlinearities. Simple sufficient conditions are provided enable us to obtain infinitely many distinct subharmonic solutions. Our approach is based on a variational method, in particular the saddle point theorem.

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