-
Previous Article
On the problem of positive predecessor density in $3n+1$ dynamics
- DCDS Home
- This Issue
-
Next Article
A note on limit laws for minimal Cantor systems with infinite periodic spectrum
Periodic solutions of the second order differential equations with asymmetric nonlinearities depending on the derivatives
| 1. | Department of Mathematics, Capital Normal University, Beijing 100037, China |
$x''+a x^+ - b x^-$ $ + g(x')=p(t),$
$x''+a x^+ - b x^-$ $ + f(x)+g(x')=p(t),$
where $(a, b)$ lies on one of the Fučik spectrum curves. We provide sufficient conditions for the existence of periodic solutions for the given equations if the limits $\lim_{x\to+\infty}g(x)=g(+\infty), \lim_{x\to-\infty}g(x)=g(-\infty)$ and $\lim_{x\to+\infty}f(x)=f(+\infty)$, $\lim_{x\to-\infty}f(x)=f(-\infty)$ exist and are finite. We also prove that the former equation has at least one periodic solution if $g(x)$ satisfies sublinear condition and that the latter equation has at least one periodic solution if $g(x)$ is bounded and $f(x)$ satisfies subquadratic condition.
| [1] |
Zhengxin Zhou. On the Poincaré mapping and periodic solutions of nonautonomous differential systems. Communications on Pure & Applied Analysis, 2007, 6 (2) : 541-547. doi: 10.3934/cpaa.2007.6.541 |
| [2] |
Zalman Balanov, Meymanat Farzamirad, Wieslaw Krawcewicz, Haibo Ruan. Applied equivariant degree. part II: Symmetric Hopf bifurcations of functional differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 16 (4) : 923-960. doi: 10.3934/dcds.2006.16.923 |
| [3] |
Fabrizio Colombo, Irene Sabadini, Frank Sommen. The inverse Fueter mapping theorem. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1165-1181. doi: 10.3934/cpaa.2011.10.1165 |
| [4] |
John Banks. Topological mapping properties defined by digraphs. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 83-92. doi: 10.3934/dcds.1999.5.83 |
| [5] |
Mads Kyed. On a mapping property of the Oseen operator with rotation. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1315-1322. doi: 10.3934/dcdss.2013.6.1315 |
| [6] |
Apostolis Pavlou. Asymmetric information in a bilateral monopoly. Journal of Dynamics & Games, 2016, 3 (2) : 169-189. doi: 10.3934/jdg.2016009 |
| [7] |
Armands Gritsans, Felix Sadyrbaev. The Nehari solutions and asymmetric minimizers. Conference Publications, 2015, 2015 (special) : 562-568. doi: 10.3934/proc.2015.0562 |
| [8] |
V. Afraimovich, J. Schmeling, Edgardo Ugalde, Jesús Urías. Spectra of dimensions for Poincaré recurrences. Discrete & Continuous Dynamical Systems - A, 2000, 6 (4) : 901-914. doi: 10.3934/dcds.2000.6.901 |
| [9] |
Yangjian Sun, Changjian Liu. The Poincaré bifurcation of a SD oscillator. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020173 |
| [10] |
Eva Miranda, Romero Solha. A Poincaré lemma in geometric quantisation. Journal of Geometric Mechanics, 2013, 5 (4) : 473-491. doi: 10.3934/jgm.2013.5.473 |
| [11] |
Mike Boyle, Sompong Chuysurichay. The mapping class group of a shift of finite type. Journal of Modern Dynamics, 2018, 13: 115-145. doi: 10.3934/jmd.2018014 |
| [12] |
Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure & Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655 |
| [13] |
Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure & Applied Analysis, 2006, 5 (3) : 515-528. doi: 10.3934/cpaa.2006.5.515 |
| [14] |
D. Bonheure, C. Fabry. A variational approach to resonance for asymmetric oscillators. Communications on Pure & Applied Analysis, 2007, 6 (1) : 163-181. doi: 10.3934/cpaa.2007.6.163 |
| [15] |
Lixia Wang, Shiwang Ma. Unboundedness of solutions for perturbed asymmetric oscillators. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 409-421. doi: 10.3934/dcdsb.2011.16.409 |
| [16] |
Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure & Applied Analysis, 2007, 6 (1) : 69-82. doi: 10.3934/cpaa.2007.6.69 |
| [17] |
João Lopes Dias. Brjuno condition and renormalization for Poincaré flows. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 641-656. doi: 10.3934/dcds.2006.15.641 |
| [18] |
Antonio Giorgilli, Stefano Marmi. Convergence radius in the Poincaré-Siegel problem. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 601-621. doi: 10.3934/dcdss.2010.3.601 |
| [19] |
Dirk Pauly. On Maxwell's and Poincaré's constants. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 607-618. doi: 10.3934/dcdss.2015.8.607 |
| [20] |
William Clark, Anthony Bloch, Leonardo Colombo. A Poincaré-Bendixson theorem for hybrid systems. Mathematical Control & Related Fields, 2020, 10 (1) : 27-45. doi: 10.3934/mcrf.2019028 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]