Existence of 2π-periodic solutions for the non-dissipative Duffing equation under asymptotic behaviors of potential function

2005 ◽  
Vol 57 (1) ◽  
pp. 1-11 ◽  
Author(s):  
W. B. Liu ◽  
Y. Li
Keyword(s):  
Periodic Solutions ◽  
Potential Function ◽  
Duffing Equation ◽  
Asymptotic Behaviors

scholarly journals Periodic orbits in virtually contact structures

2018 ◽  
Vol 12 (02) ◽  
pp. 371-418
Author(s):  
Youngjin Bae ◽  
Kevin Wiegand ◽  
Kai Zehmisch
Keyword(s):  
Periodic Solutions ◽  
Potential Function ◽  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Contact Structure ◽  
Critical Value ◽  
Holomorphic Curves ◽  
Contact Structures ◽  
Contact Form ◽  
Contact Manifolds

We prove that certain non-exact magnetic Hamiltonian systems on products of closed hyperbolic surfaces and with a potential function of large oscillation admit non-constant contractible periodic solutions of energy below the Mañé critical value. For that we develop a theory of holomorphic curves in symplectizations of non-compact contact manifolds that arise as the covering space of a virtually contact structure whose contact form is bounded with all derivatives up to order three.

Periodic solutions of the Duffing equation

2008 ◽  
Vol 30 (5) ◽  
pp. 593-602
Author(s):  
Jale Tezcan ◽  
J. Kent Hsiao
Keyword(s):  
Periodic Solutions ◽  
Duffing Equation

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

Positive periodic solutions to the forced non-autonomous Duffing equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiří Šremr
Keyword(s):  
Periodic Solutions ◽  
Positive Solutions ◽  
Periodic Problem ◽  
Duffing Equation ◽  
Positive Periodic Solutions ◽  
Duffing Equations ◽  
Existence And Multiplicity ◽  
Constant Coefficients ◽  
Multiplicity Of Positive Solutions

Abstract We study the existence and multiplicity of positive solutions to the periodic problem for a forced non-autonomous Duffing equation u ′′ = p ⁢ ( t ) ⁢ u - h ⁢ ( t ) ⁢ | u | λ ⁢ sgn ⁡ u + f ⁢ ( t ) ; u ⁢ ( 0 ) = u ⁢ ( ω ) , u ′ ⁢ ( 0 ) = u ′ ⁢ ( ω ) , u^{\prime\prime}=p(t)u-h(t)\lvert u\rvert^{\lambda}\operatorname{sgn}u+f(t);\quad u(0)=u(\omega),\ u^{\prime}(0)=u^{\prime}(\omega), where p , h , f ∈ L ⁢ ( [ 0 , ω ] ) p,h,f\in L([0,\omega]) and λ > 1 \lambda>1 . The obtained results are compared with the results known for the equations with constant coefficients.

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