scholarly journals Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations with Superlinear Nonlinearities

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Yongxiang Li ◽  
Lanjun Guo
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Existence Result ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Superlinear Growth ◽  
Existence Of Periodic Solutions

This paper is concerned with the existence of periodic solutions for the fully second-order ordinary differential equation u′′(t)=ft,ut,u′t, t∈R, where the nonlinearity f:R3→R is continuous and f(t,x,y) is 2π-periodic in t. Under certain inequality conditions that f(t,x,y) may be superlinear growth on (x,y), an existence result of odd 2π-periodic solutions is obtained via Leray-Schauder fixed point theorem.

NONDEGENERACY OF THE PERIODICALLY FORCED LIÉNARD DIFFERENTIAL EQUATION WITH ϕ-LAPLACIAN

2011 ◽  
Vol 13 (02) ◽  
pp. 283-292 ◽  
Author(s):  
P. J. TORRES
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Multiplicity Results ◽  
Related Literature ◽  
Pendulum Equation ◽  
Existence Of Periodic Solutions ◽  
Schäuder Fixed Point Theorem

New results on the existence of periodic solutions of a forced Liénard differential equation with ϕ-Laplacian are provided. The method of proof relies on the Schauder fixed point theorem, so some information on the location of the solutions is also obtained, leading to multiplicity results. The flexibility of this approach is tested by comparing our results with some examples taken from the related literature, including the classical pendulum equation.

scholarly journals A Note on Periodic Solutions of Second Order Nonautonomous Singular Coupled Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Zhongwei Cao ◽  
Chengjun Yuan ◽  
Daqing Jiang ◽  
Xiaowei Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Coupled Systems ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Periodic Solutions

We establish the existence of periodic solutions of the second order nonautonomous singular coupled systemsx′′+a1(t)x=f1(t,y(t))+e1(t)for a.e.t∈[0,T],y′′+a2(t)y=f2(t,x(t))+e2(t)for a.e.t∈[0,T]. The proof relies on Schauder's fixed point theorem.

scholarly journals Positive periodic solutions for second-order neutral differential equations with time-dependent deviating arguments

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3627-3638 ◽  
Author(s):  
Zhibo Cheng ◽  
Feifan Li ◽  
Shaowen Yao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Time Dependent ◽  
Positive Periodic Solutions ◽  
Deviating Arguments ◽  
Neutral Differential Equations

In this paper, we consider a kind of second-order neutral differential equation with timedependent deviating arguments. By applications of Krasnoselskii?s fixed point theorem, sufficient conditions for the existence of positive periodic solutions are established.

scholarly journals Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

scholarly journals Periodic Solutions and Nontrivial Periodic Solutions for a Class of Rayleigh-Type Equation with Two Deviating Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Meiqiang Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Type Equation ◽  
Index Theorem ◽  
Rayleigh Equation ◽  
Deviating Arguments ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions

The Rayleigh equation with two deviating argumentsx′′(t)+f(x'(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=e(t)is studied. By using Leray-Schauder index theorem and Leray-Schauder fixed point theorem, we obtain some new results on the existence of periodic solutions, especially for the existence of nontrivial periodic solutions to this equation. The results are illustrated with two examples, which cannot be handled using the existing results.

scholarly journals Existence and Lyapunov Stability of Positive Periodic Solutions for a Third-Order Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Yueli Chen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Lyapunov Stability ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Positive Periodic Solutions ◽  
Third Order

By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

scholarly journals On the Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and their Relation to the MHD Continuum

1982 ◽  
Vol 37 (8) ◽  
pp. 830-839 ◽  
Author(s):  
A. Salat
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Infinite Sequence ◽  
Periodic Coefficient ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Magnetic Surfaces ◽  
Toroidal Geometry

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{ω1t, ω2t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω1, ω2, a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained.The equation considered is a model for the magneto-hydrodynamic “continuum” in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently ir-rational magnetic surfaces

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