Andres, Jan Solution with periodic second derivative of a certain third order differential equation. (English) Zbl 0629.34048 Math. Slovaca 37, 239-245 (1987). Sufficient conditions for the existence of periodic solutions of the third kind, i.e. those with the second periodic derivative, to the equation \(x\prime''+ax''+g(t,x')+cx=p(t)\), where a, c are constants, \(g(t,y+w)\equiv g(t+T,y)\equiv g(t,y)\in {\mathfrak C}^ 1(R^ 2)\) and p(t)\(\in {\mathfrak C}^ 1({\mathbb{R}}^ 1)\) is of the special (necessary) form, are given using a topological degree argument. This problem is solvable for \(0\neq | c| <| T|^{-3}\). Cited in 1 Document MSC: 34C25 Periodic solutions to ordinary differential equations Keywords:periodic solutions of the third kind; topological degree PDFBibTeX XMLCite \textit{J. Andres}, Math. Slovaca 37, 239--245 (1987; Zbl 0629.34048) Full Text: EuDML References: [1] FARKAS M.: Controllably periodic perturbations of autonomous systems. Acta Math. Acad. Sci. Hungar., 22, 1971, 337-348. · Zbl 0239.34016 · doi:10.1007/BF01896427 [2] FARKAS M.: Determination of controllably periodic perturbed solutions by Poincaré’s method. Stud. Sci. Math. Hungar., 7, 1972, 257-266. · Zbl 0275.34038 [3] FARKAS M.: Personal communication. [4] ANDRES J.: Periodic boundary value problem for certain nonlinear differential equations of the third order. Math. Slovaca, 3, 35, 1985, 305-309. · Zbl 0591.34037 [5] ANDRES J., VORÁČEK J.: Periodic solutions to a nonlinear parametric differential equation of the third order. Atti Accad. Naz. Lincei, 3-4, 77, 81-86. [6] ANDRES J.: Periodic derivative of solutions to nonlinear differential equations. to appear in Czech. Math. J. · Zbl 0727.34029 [7] MAWHIN J.: Topological degree methods in nonlinear boundary value problems. CBMS 40, AMS, Providence 1979. · Zbl 0414.34025 [8] ANDRES. J., VORÁČEK J.: Periodic solutions of a certain parametric third order differential equation. Kniž. odb. věd. sp. VUT v Brné, B94, 1983, 7-11. [9] REISSIG R.: Continua of periodic solutions of the Liénard equation. Constr. meth. nonlin. BVPs and nonlin. oscill. (ed. J. Albrecht, L. Collatz, K. Kirchgässner), Birkhäuser, Basel 1979, pp. 126-133. · Zbl 0416.34045 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.