Infinitely many periodic solutions of Duffing equations under integral condition

2020 ◽  
pp. 1
Author(s):  
Nannan Zheng ◽  
Zaihong Wang
Keyword(s):  
Periodic Solutions ◽  
Integral Condition ◽  
Duffing Equations ◽  
Infinitely Many Periodic Solutions

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.

scholarly journals Infinitely many periodic solutions for a semilinear wave equation with x-dependent coefficients

2020 ◽  
Vol 26 ◽  
pp. 7
Author(s):  
Hui Wei ◽  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Spectral Properties ◽  
Seismic Waves ◽  
Forced Vibrations ◽  
One Dimensional ◽  
Semilinear Wave Equation ◽  
Spatial Interval ◽  
Rational Multiple ◽  
Infinitely Many Periodic Solutions

This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with x-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media. By combining variational methods with an approximation argument, we prove that there exist infinitely many periodic solutions whenever the period is a rational multiple of the length of the spatial interval. The proof is essentially based on the spectral properties of the wave operator with x-dependent coefficients.

Infinitely many periodic solutions for ordinary p-Laplacian systems

2015 ◽  
Vol 4 (4) ◽  
pp. 251-261 ◽  
Author(s):  
Chun Li ◽  
Ravi P. Agarwal ◽  
Chun-Lei Tang
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Existence Theorems ◽  
Point Theory ◽  
Minimax Methods ◽  
Infinitely Many Periodic Solutions

AbstractSome existence theorems are obtained for infinitely many periodic solutions of ordinary p-Laplacian systems by minimax methods in critical point theory.

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