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 Applications of Schauder’s Fixed Point Theorem to Semipositone Singular Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Zhongwei Cao ◽  
Chengjun Yuan ◽  
Xiuling Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Schauder’S Fixed Point Theorem ◽  
Singular Differential Equations ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Periodic Solutions ◽  
Weak Singularities

We study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results generalized and extended those results contained in the studies by Chu and Torres (2007) and Torres (2007) . In some suitable weak singularities, the existence of periodic solutions may help.

scholarly journals PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

scholarly journals Existence and Attractivity Results for Coupled Systems of Nonlinear Volterra–Stieltjes Multidelay Fractional Partial Integral Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Naima Hamidi ◽  
Gaston N’Guérékata
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Coupled Systems ◽  
Schauder’S Fixed Point Theorem ◽  
Integral System ◽  
Schauder's Fixed Point Theorem ◽  
Globally Attractive

We are concerned with some existence and attractivity results of a coupled fractional Riemann–Liouville–Volterra–Stieltjes multidelay partial integral system. We prove the existence of solutions using Schauder’s fixed point theorem; then we show that the solutions are uniformly globally attractive.

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 Uniqueness of Periodic Solutions for Second Order Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yuanhong Wei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Function Space ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Second Order Differential Equations

We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.

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.

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