Pan, Lijun Periodic solutions for higher order differential equations with deviating argument. (English) Zbl 1160.34065 J. Math. Anal. Appl. 343, No. 2, 904-918 (2008). By using a continuation theorem in coincidence degree theory, the author derives some new criteria for the existence of periodic solutions for a higher order differential equations with periodic deviating arguments. Reviewer: Meng Fan (Changchun) Cited in 9 Documents MSC: 34K13 Periodic solutions to functional-differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:higher order differential equations; deviating argument; periodic solution; coincidence degree PDFBibTeX XMLCite \textit{L. Pan}, J. Math. Anal. Appl. 343, No. 2, 904--918 (2008; Zbl 1160.34065) Full Text: DOI References: [1] Omari, P.; Villari, G.; Zanolin, F., Periodic solutions of Lienard equation with one-side growth restrictions, J. Differential Equations, 67, 278-293 (1987) · Zbl 0615.34037 [2] Mawhin, J., An extension of a theorem of A.C. Lazer on forced nonlinear oscillations, J. Math. Anal. Appl., 40, 20-29 (1972) · Zbl 0245.34035 [3] Mawhin, J., Degré topologique et solutions périodiques des systémes différentiels nonlineares, Bull. Soc. Roy. Sci. Liége, 38, 308-398 (1969) · Zbl 0186.41704 [4] Cong, F., Periodic solutions for \(2k\) th order ordinary differential equations with resonance, Nonlinear Anal., 32, 787-793 (1998) · Zbl 0980.34040 [5] Cong, F., Existence of \((2 k + 1)\) th order ordinary differential equations, Appl. Math. Lett., 17, 727-732 (2004) · Zbl 1071.34038 [6] Liu, W. B.; Li, Y., The existence of periodic solutions for high order duffing equations, Acta Math. Sinica, 46, 49-56 (2003), (in Chinese) · Zbl 1036.34052 [7] Liu, B. W.; Huang, L. H., Existence of periodic solutions for nonlinear \(n\) th order ordinary differential equations, Acta Math. Sinica, 47, 1133-1140 (2004), (in Chinese) · Zbl 1124.34334 [8] Liu, Z. L., Periodic solution for nonlinear \(n\) th order ordinary differential equation, J. Math. Anal. Appl., 204, 46-64 (1996) · Zbl 0873.34032 [9] Cong, F.; Huang, Q. D.; Shi, S. Y., Existence and uniqueness of periodic solutions for \((2 n + 1)\) th order ordinary differential equations, J. Math. Anal. Appl., 241, 1-9 (2000) · Zbl 0944.34036 [10] Lu, S.; Ge, W., On the existence of periodic solutions for Lienard equation with a deviating argument, J. Math. Anal. Appl., 289, 241-243 (2004) · Zbl 1054.34114 [11] Lu, S.; Ge, W., Sufficient conditions for the existence of periodic solutions to some second order differential equation with a deviating argument, J. Math. Anal. Appl., 308, 393-419 (2005) · Zbl 1087.34048 [12] Wang, G. Q., A priori bounds for periodic solutions of a delay Rayleigh equation, Appl. Math. Lett., 12, 41-44 (1999) · Zbl 0980.34068 [13] Fabry, C.; Mawhin, J. L.; Nkashama, M. N., A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations, Bull. London Math. Soc., 10, 173-180 (1986) · Zbl 0586.34038 [14] Jiao, G., Periodic solutions of \((2 n + 1)\) th order ordinary differential equations, J. Math. Anal. Appl., 272, 691-699 (2004) [15] Kiguradze, I. T.; Puza, B., On periodic solutions of system of differential equations with deviating arguments, Nonlinear Anal., 42, 229-242 (2000) · Zbl 0966.34066 [16] Srzednicki, S., On periodic solutions of certain \(n\) th differential equations, J. Math. Anal. Appl., 196, 666-675 (1995) · Zbl 0844.34037 [17] Wang, G. Q., Existence theorems of periodic solutions for a delay nonlinear differential equation with piecewise constant argument, J. Math. Anal. Appl., 298, 298-307 (2004) · Zbl 1071.34071 [18] Liu, Y. J.; Yang, P. H.; Ge, W. G., Periodic solutions of high-order delay differential equations, Nonlinear Anal., 63, 136-152 (2005) · Zbl 1088.34061 [19] Ren, J. L.; Ge, W. G., On the existence of periodic solutions for the second order functional differential equation, Acta Math. Sinica, 47, 569-578 (2004), (in Chinese) · Zbl 1387.34099 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.