del Pino, Manuel A.; Manásevich, Raúl; Montero, Alberto \(T\)-periodic solutions for some second order differential equations with singularities. (English) Zbl 0761.34031 Proc. R. Soc. Edinb., Sect. A 120, No. 3-4, 231-243 (1992). The authors study the existence of \(T\)-periodic positive solutions of the equation (1) \(x''+f(t,x)=0\) where \(f: \mathbb R\times \mathbb R^ +\to \mathbb R\) is a continuous function, \(T\)-periodic in the first variable, and \(f(t,.)\) has a singularity of repulsive type near the origin. Under the assumption that \(f(t,x)\) lies between two lines of positive slope for large and positive \(x\), they are given in Theorem 1.1 a new non-resonance condition which predicts the existence of one \(T\)-periodic solution of (1). The proof of Theorem 1.1 is based on degree theory together with oscillatory properties of “large” solutions of equation (1). The authors devote this paper to the proof of this result. Reviewer: C.D.Chirila (Iaşi) Cited in 2 ReviewsCited in 61 Documents MSC: 34C25 Periodic solutions to ordinary differential equations Keywords:existence of \(T\)-periodic positive solutions; singularity of repulsive type; non-resonance condition; degree theory; oscillatory properties PDFBibTeX XMLCite \textit{M. A. del Pino} et al., Proc. R. Soc. Edinb., Sect. A, Math. 120, No. 3--4, 231--243 (1992; Zbl 0761.34031) Full Text: DOI References: [1] DOI: 10.1016/0362-546X(90)90037-H · Zbl 0708.34041 · doi:10.1016/0362-546X(90)90037-H [2] DOI: 10.1090/S0002-9939-1987-0866438-7 · doi:10.1090/S0002-9939-1987-0866438-7 [3] Ambrosseti, Analisi Non Lineare (1973) [4] DOI: 10.1016/0022-1236(89)90078-5 · Zbl 0681.70018 · doi:10.1016/0022-1236(89)90078-5 [5] DOI: 10.1016/0022-247X(88)90022-4 · Zbl 0672.34030 · doi:10.1016/0022-247X(88)90022-4 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.