# American Institute of Mathematical Sciences

July  2017, 16(4): 1471-1492. doi: 10.3934/cpaa.2017070

## On the set of harmonic solutions of a class of perturbed coupled and nonautonomous differential equations on manifolds

 Dipartimento di Matematica e Informatica "Ulisse Dini", Via S. Marta 3,50139 Firenze, Italy

Received  July 2016 Revised  February 2017 Published  April 2017

Fund Project: The authors have been supported by the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)

We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed coupled and nonautonomous differential equations on manifolds. By using degree-theoretic methods we obtain a global continuation result for the $T$-periodic solutions of the considered equations.

Citation: Luca Bisconti, Marco Spadini. On the set of harmonic solutions of a class of perturbed coupled and nonautonomous differential equations on manifolds. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1471-1492. doi: 10.3934/cpaa.2017070
##### References:

show all references

##### References:
Initial points of $2\pi$-periodic solutions of (2): Nontrivial $2\pi$-periodic solutions correspond to points with $\lambda>0$
The system of Example 3.5
Projections of the set of starting triples of (2)
The mechanical system of Example 6.2
 [1] Marco Spadini. Branches of harmonic solutions to periodically perturbed coupled differential equations on manifolds. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 951-964. doi: 10.3934/dcds.2006.15.951 [2] Alfonso Castro, Rosa Pardo. Branches of positive solutions of subcritical elliptic equations in convex domains. Conference Publications, 2015, 2015 (special) : 230-238. doi: 10.3934/proc.2015.0230 [3] Jaume Llibre, Luci Any Roberto. On the periodic solutions of a class of Duffing differential equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 277-282. doi: 10.3934/dcds.2013.33.277 [4] Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3127-3144. doi: 10.3934/dcdsb.2017167 [5] Rafael Ortega. Stability and index of periodic solutions of a nonlinear telegraph equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 823-837. doi: 10.3934/cpaa.2005.4.823 [6] Juan Campos, Rafael Ortega. Location of fixed points and periodic solutions in the plane. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 517-523. doi: 10.3934/dcdsb.2008.9.517 [7] Xianhua Huang. Almost periodic and periodic solutions of certain dissipative delay differential equations. Conference Publications, 1998, 1998 (Special) : 301-313. doi: 10.3934/proc.1998.1998.301 [8] Nguyen Minh Man, Nguyen Van Minh. On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations. Communications on Pure & Applied Analysis, 2004, 3 (2) : 291-300. doi: 10.3934/cpaa.2004.3.291 [9] Yong Li, Zhenxin Liu, Wenhe Wang. Almost periodic solutions and stable solutions for stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-18. doi: 10.3934/dcdsb.2019113 [10] Hernán R. Henríquez, Claudio Cuevas, Alejandro Caicedo. Asymptotically periodic solutions of neutral partial differential equations with infinite delay. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2031-2068. doi: 10.3934/cpaa.2013.12.2031 [11] Miguel V. S. Frasson, Patricia H. Tacuri. Asymptotic behaviour of solutions to linear neutral delay differential equations with periodic coefficients. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1105-1117. doi: 10.3934/cpaa.2014.13.1105 [12] Feliz Minhós. Periodic solutions for some fully nonlinear fourth order differential equations. Conference Publications, 2011, 2011 (Special) : 1068-1077. doi: 10.3934/proc.2011.2011.1068 [13] Jean Mawhin, James R. Ward Jr. Guiding-like functions for periodic or bounded solutions of ordinary differential equations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 39-54. doi: 10.3934/dcds.2002.8.39 [14] Adam Lipowski, Bogdan Przeradzki, Katarzyna Szymańska-Dębowska. Periodic solutions to differential equations with a generalized p-Laplacian. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2593-2601. doi: 10.3934/dcdsb.2014.19.2593 [15] Zhiming Guo, Xiaomin Zhang. Multiplicity results for periodic solutions to a class of second order delay differential equations. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1529-1542. doi: 10.3934/cpaa.2010.9.1529 [16] Tomás Caraballo, David Cheban. Almost periodic and almost automorphic solutions of linear differential equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 1857-1882. doi: 10.3934/dcds.2013.33.1857 [17] Vera Ignatenko. Homoclinic and stable periodic solutions for differential delay equations from physiology. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3637-3661. doi: 10.3934/dcds.2018157 [18] Jaume Llibre, Amar Makhlouf. Periodic solutions of some classes of continuous second-order differential equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 477-482. doi: 10.3934/dcdsb.2017022 [19] Zaihong Wang. Periodic solutions of the second order differential equations with asymmetric nonlinearities depending on the derivatives. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 751-770. doi: 10.3934/dcds.2003.9.751 [20] Changrong Zhu, Bin Long. The periodic solutions bifurcated from a homoclinic solution for parabolic differential equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3793-3808. doi: 10.3934/dcdsb.2016121

2017 Impact Factor: 0.884

## Metrics

• HTML views (2)
• Cited by (1)

• on AIMS