A priori bounds for periodic solutions of a Duffing equation

2008 ◽  
Vol 26 (1-2) ◽  
pp. 535-543 ◽  
Author(s):  
Xinmin Wu ◽  
Jingwen Li ◽  
Yong Zhou
Keyword(s):  
Periodic Solutions ◽  
A Priori ◽  
Duffing Equation ◽  
A Priori Bounds

scholarly journals Periodic solution for ϕ-Laplacian neutral differential equation

2019 ◽  
Vol 17 (1) ◽  
pp. 172-190 ◽  
Author(s):  
Shaowen Yao ◽  
Zhibo Cheng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
A Priori ◽  
Neutral Differential Equation ◽  
A Priori Bounds ◽  
T Tau

Abstract This paper is devoted to the existence of a periodic solution for ϕ-Laplacian neutral differential equation as follows $$\begin{array}{} (\phi(x(t)-cx(t-\tau))')'=f(t,x(t),x'(t)). \end{array}$$ By applications of an extension of Mawhin’s continuous theorem due to Ge and Ren, we obtain that given equation has at least one periodic solution. Meanwhile, the approaches to estimate a priori bounds of periodic solutions are different from the corresponding ones of the known literature.

scholarly journals A priori bounds for periodic solutions of a delay Rayleigh equation with damping

2003 ◽  
Vol 34 (3) ◽  
pp. 293-298
Author(s):  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Periodic Solutions ◽  
Existence Theorems ◽  
A Priori ◽  
Continuation Theorem ◽  
Rayleigh Equation ◽  
A Priori Bounds ◽  
Mawhin’S Continuation Theorem ◽  
Equation With Delay

A priori bounds are established for periodic solutions of a Rayleigh equation with delay and damping. Such bounds are useful since existence theorems for periodic solutions can then be obtained by means of Mawhin's continuation theorem.

CONTINUATION THEOREMS FOR AMBROSETTI-PRODI TYPE PERIODIC PROBLEMS

2000 ◽  
Vol 02 (01) ◽  
pp. 87-126 ◽  
Author(s):  
JEAN MAWHIN ◽  
CARLOTA REBELO ◽  
FABIO ZANOLIN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
A Priori ◽  
Nonlinear Ordinary Differential Equations ◽  
Type Problem ◽  
Normed Spaces ◽  
A Priori Bounds ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions

We study the existence of periodic solutions u(·) for a class of nonlinear ordinary differential equations depending on a real parameter s and obtain the existence of closed connected branches of solution pairs (u, s) to various classes of problems, including some cases, like the superlinear one, where there is a lack of a priori bounds. The results are obtained as a consequence of a new continuation theorem for the coincidence equation Lu=N(u, s) in normed spaces. Among the applications, we discuss also an example of existence of global branches of periodic solutions for the Ambrosetti–Prodi type problem u″+g(u)=s+ p(t), with g satisfying some asymmetric conditions.

On periodic solutions of nonlinear second order vector differential equations

1986 ◽  
Vol 104 (1-2) ◽  
pp. 107-125 ◽  
Author(s):  
P. Habets ◽  
M. N. Nkashama
Keyword(s):  
Linear Operator ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Periodic Solutions ◽  
Symmetric Matrix ◽  
A Priori ◽  
Degree Theory ◽  
Duffing Equation ◽  
Existence Of Periodic Solutions ◽  
Image Position

SynopsisThis paper considers existence of periodic solutions for vector Liénard differential equationsIn our main result we writewhere Q(t, x) is a symmetric matrix and h(t, x) is sublinear. The key assumption relates the asymptotic behaviour as x →+ ∞ of the eigenvalues of Q(t, x) to the spectrum of the linear operator −d2/dt2 Several choices for Q(t, x) are considered which lead to known theorems and extend others. In the case of the Duffing equationthe assumptions are weakened.Our approach is based on Leray-Schauder's degree theory and a priori estimates.

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