Existence of multiplicity harmonic and subharmonic solutions for second-order quasilinear equation via Poincaré-Birkhoff twist theorem

2017 ◽  
Vol 40 (18) ◽  
pp. 6801-6822
Author(s):  
Zhibo Cheng ◽  
Jingli Ren
Keyword(s):  
Quasilinear Equation ◽  
Second Order ◽  
Subharmonic Solutions ◽  
Twist Theorem

scholarly journals Harmonic and subharmonic solutions of quadratic Liénard type systems with sublinearity

2021 ◽  
Vol 6 (11) ◽  
pp. 12913-12928
Author(s):  
Chunmei Song ◽  
◽  
Qihuai Liu ◽  
Guirong Jiang ◽  
Keyword(s):  
Differential Equations ◽  
Type Systems ◽  
Second Order ◽  
Subharmonic Solutions ◽  
Twist Theorem

<abstract><p>In this paper, we prove the existence of harmonic solutions and infinitely many subharmonic solutions of dissipative second order sublinear differential equations named quadratic Liénard type systems. The method of the proof is based on the Poincaré-Birkhoff twist theorem.</p></abstract>

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>

One-Signed Harmonic Solutions and Sign-Changing Subharmonic Solutions to Scalar Second Order Differential Equations

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Alberto Boscaggin
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Point Theorem ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Subharmonic Solutions

AbstractUsing a recent modified version of the Poincaré-Birkhoff fixed point theorem [19], we study the existence of one-signed T-periodic solutions and sign-changing subharmonic solutions to the second order scalar ODEu′′ + f (t, u) = 0,being f : ℝ × ℝ → ℝ a continuous function T-periodic in the first variable and such that f (t, 0) ≡ 0. Partial extensions of the results to a general planar Hamiltonian systems are given, as well.

Bouncing solutions of an equation with attractive singularity

2004 ◽  
Vol 134 (1) ◽  
pp. 201-213 ◽  
Author(s):  
Dingbian Qian ◽  
Pedro J. Torres
Keyword(s):  
Periodic Solutions ◽  
Second Order ◽  
Attractive Singularity ◽  
Twist Theorem

For any n, m ∈ N, we prove the existence of 2mπ-periodic solutions, with n bouncings in each period, for a second-order forced equation with attractive singularity by using the approach of successor map and Poincaré-Birkhoff twist theorem.

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