Periodic Solutions of Discontinuous Duffing Equations

2020 ◽  
Vol 19 (3) ◽  
Author(s):  
Fangfang Jiang
Keyword(s):  
Periodic Solutions ◽  
Duffing Equations

scholarly journals Infinitely Many Periodic Solutions of Duffing Equations with Singularities via Time Map

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Tiantian Ma ◽  
Zaihong Wang
Keyword(s):  
Periodic Solutions ◽  
Autonomous System ◽  
Positive Periodic Solutions ◽  
Duffing Equations ◽  
Time Map ◽  
Twist Theorem ◽  
The Given ◽  
Infinitely Many Periodic Solutions

We study the periodic solutions of Duffing equations with singularitiesx′′+g(x)=p(t). By using Poincaré-Birkhoff twist theorem, we prove that the given equation possesses infinitely many positive periodic solutions provided thatgsatisfies the singular condition and the time map related to autonomous systemx′′+g(x)=0tends to zero.

Coincidence degree and periodic solutions of Duffing equations

1998 ◽  
Vol 34 (3) ◽  
pp. 443-460 ◽  
Author(s):  
Ma Shiwang ◽  
Wang Zhicheng ◽  
Yu Jianshe
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Duffing Equations

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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