Periodic solutions for periodic second-ordervdifferential equations with variable potentials

• Autorzy: Llibre J. , Makhlouf A.

Identyfikatory

DOI

10.1515/jaa-2018-0013

• Języki publikacji: EN

Abstrakty

EN

We provide sufficient conditions for the existence of periodic solutions of the second-order differentia equation with variable potentials −(px’)’(t) − r(t)p(t)x’(t) + q(t)x(t) = f(t, x(t)), where the functions p(t) > 0, q(t), r(t) and f(t, x) are C2 and T-periodic in the variable t.

Słowa kluczowe

EN

periodic orbits; third-order differential equation; quadratic system; averaging theory

PL

orbita periodyczna; równanie różniczkowe trzeciego rzędu; układ kwadratowy; teoria uśredniania

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2018
• Tom: Vol. 24, nr 2
• Strony: 127--137
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Llibre J.

• Departament de Matematiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain

autor

Makhlouf A.

• Department of Mathematics, University of Annaba, Elhadjar 23 Annaba, Algeria

Bibliografia

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• [2] D. R. Anderson, Multiple periodic solutions for a second-order problem on periodic time scales, Nonlinear Anal. 60 (2005), no. 1, 101-115.
• [3] D. R. Anderson and R. I. Avery, Existence of a periodic solution for continuous and discrete periodic second-order equations with variable potentials, J. Appl. Math. Comput. 37 (2011), 297-312.
• [4] A. Buica, J. P. Françoise and J. Llibre, Periodic solutions of nonlinear periodic differential systems with a small parameter, Commun. Pure Appl. Anal. 6 (2006), 103-111.
• [5] J. R. Graef, L. Kong and H. Wang, Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem, J. Differential Equations 245 (2008), 1185-1197.
• [6] Y. Liu, W. Ge and Z. Gui, Three positive periodic solutions of nonlinear differential equations with periodic coefficients, Anal. Appl. 3 (2005), no. 2, 145-155.
• [7] I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations (in Russian), Gosudarstv. Izdat. Tehn-Teor. Lit., Moscow, 1956.
• [8] M. Roseau, Vibrations non linéaires et théorie de la stabilité, Springer Tracts Nat. Philos. 8, Springer, New York, 1985.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).