scholarly journals A Bifurcation Phenomenon for the Periodic Solutions of the Duffing Equation without Damping Terms

2003 ◽  
Vol 9 (2) ◽  
pp. 259-268
Author(s):  
Yoshifumi TAKENOUCHI
Keyword(s):  
Periodic Solutions ◽  
Duffing Equation ◽  
Bifurcation Phenomenon

scholarly journals A Bifurcation phenomenon for the periodic solutions of the Duffing equation

1997 ◽  
Vol 37 (2) ◽  
pp. 191-209
Author(s):  
Yukie Komatsu ◽  
Tadayoshi Kano ◽  
Akitaka Matsumura
Keyword(s):  
Periodic Solutions ◽  
Duffing Equation ◽  
Bifurcation Phenomenon

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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