Subharmonic Solutions of a Pendulum Under Vertical Anharmonic Oscillations of the Point of Suspension

2017 ◽  
Vol 22 (7) ◽  
pp. 782-791
Author(s):  
Hildeberto E. Cabral ◽  
Tiago de A. Amorim
Keyword(s):  
Subharmonic Solutions ◽  
Anharmonic Oscillations

scholarly journals Subharmonic solutions of bounded coupled Hamiltonian systems with sublinear growth

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fanfan Chen ◽  
Dingbian Qian ◽  
Xiying Sun ◽  
Yinyin Wu
Keyword(s):  
Hamiltonian Systems ◽  
Phase Plane ◽  
Phase Plane Analysis ◽  
Zero Eigenvalue ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Plane Analysis ◽  
Higher Dimensional ◽  
Dimensional Version ◽  
Twist Theorem

<p style='text-indent:20px;'>We prove the existence and multiplicity of subharmonic solutions for bounded coupled Hamiltonian systems. The nonlinearities are assumed to satisfy Landesman-Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is based on phase plane analysis and a higher dimensional version of the Poincaré-Birkhoff twist theorem by Fonda and Ureña. The results obtained generalize the previous works for scalar second-order differential equations or relativistic equations to higher dimensional systems.</p>

scholarly journals Periodic and subharmonic solutions for a 2nth-order p-Laplacian difference equation containing both advances and retardations

2018 ◽  
Vol 16 (1) ◽  
pp. 1435-1444 ◽  
Author(s):  
Peng Mei ◽  
Zhan Zhou
Keyword(s):  
Difference Equation ◽  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Nonlinear Difference Equation ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Explicit Criteria

AbstractWe consider a 2nth-order nonlinear difference equation containing both many advances and retardations with p-Laplacian. Using the critical point theory, we obtain some new explicit criteria for the existence and multiplicity of periodic and subharmonic solutions. Our results generalize and improve some known related ones.

Isochronous anharmonic oscillations

1998 ◽  
Vol 76 (8) ◽  
pp. 645-657 ◽  
Author(s):  
Pirooz Mohazzabi
Keyword(s):  
General Equation ◽  
Vertical Plane ◽  
One Dimensional ◽  
One To One ◽  
Anharmonic Oscillations ◽  
Special Case

The problem of a particle oscillating without friction on a curve in a vertical plane (referred to as a vertical curve) is addressed. It is shown that there are infinitely many asymmetric concave vertical curves on which oscillations of a particle remain isochronous. The general equation of these curves is derived, and a one-to-one correspondence between these curves and one-dimensional potentials is established. The results are compared with the existing literature, and an interesting nontrivial special case is discussed. Some issues regarding interpretation of the results in the context of action and angle variables are also addressed. PACS No. 03.20

scholarly journals Subharmonic solutions of the prescribed curvature equation

2016 ◽  
Vol 18 (03) ◽  
pp. 1550042 ◽  
Author(s):  
Chiara Corsato ◽  
Pierpaolo Omari ◽  
Fabio Zanolin
Keyword(s):  
Bounded Variation ◽  
Curvature Equation ◽  
Subharmonic Solutions ◽  
Prescribed Curvature

We study the existence of subharmonic solutions of the prescribed curvature equation [Formula: see text] According to the behavior at zero, or at infinity, of the prescribed curvature [Formula: see text], we prove the existence of arbitrarily small classical subharmonic solutions, or bounded variation subharmonic solutions with arbitrarily large oscillations.

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