×

zbMATH — the first resource for mathematics

Periodic solutions of second order nonlinear differential equations. (English) Zbl 0615.34036
The authors study the existence of periodic solutions for second order nonlinear differential equations by using the alternative method for problems at resonance as well as the method of upper and lower solutions. Some previous results are improved.

MSC:
34C25 Periodic solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] S. R. Bernfeld and V. Lakshmikantham,An Introduction to Nonlinear Boundary Value Problems, Academic Press (New York, 1974). · Zbl 0286.34018
[2] L. Cesari, Functional analysis, nonlinear differential equations and the alternative method, Proc. Conf. onNonlinear Functional Analysis and Differential Equations, (Eds. Cesari, Kannan and Schuur), Marcel Dekker, Inc., (New York, 1976), 1–197. · Zbl 0343.47038
[3] L. Cesari and R. Kannan, An abstract theorem at resonance,Proc. Amer. Math. Soc.,63 (1977), 221–225. · Zbl 0361.47021
[4] J. O. C. Ezeilo, A Leray–Schauder technique for the investigation of periodic solutions of the equation \(\ddot x + x + \mu x^2 = \varepsilon \cos \omega t(\varepsilon \neq 0)\) ,Acta Math. Acad. Sci. Hungar.,39 (1982), 59–63. · Zbl 0494.34030
[5] R. Kannan and V. Lakshmikantham, Existence of periodic solutions of nonlinear boundary value problems and the method of upper and lower solutions,Technical Report #173, University of Texas at Arlington, November 1981. · Zbl 0608.34020
[6] T. Maekawa, On a harmonic solution of \(\ddot x + x + \mu x^2 = \varepsilon \cos \omega t\) ,Math. Japonicae,13 (1968), 143–148. · Zbl 0181.09603
[7] R. Reissig, G. Sansone and R. Conti,Nonlinear Differential Equations of Higher Order, Noordhoff International Publishing (Leyden, 1974). · Zbl 0275.34001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.