Kannan, Rangachary; Nagle, R. Kent; Pothoven, Kenneth L. Remarks on the existence of solutions of \(x''+x+\arctan(x')=p(t)\); \(x(0)=x(\pi)=0\). (English) Zbl 0802.34021 Nonlinear Anal., Theory Methods Appl. 22, No. 6, 793-796 (1994). Of concern is the boundary value problem listed in the title of the paper, where \(p\) is a continuous given function. The authors use the contraction mapping principle to prove an existence and uniqueness result when \(\| p\|_ \infty\) is sufficiently small. Other conditions and approaches for existence are also discussed. Reviewer: S.Aizicovici (Athens / Ohio) Cited in 7 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:boundary value problem; contraction mapping principle; existence; uniqueness × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Kannan, R.; Ortega, R., Existence of solutions of \(x\)″ + \(x + g(x) = p(t), x(0) = 0 = x\)(π), Proc. Am. math. Soc., 96, 67-70 (1986) · Zbl 0585.34001 [2] Cesari, L., Functional analysis, nonlinear differential equations and the alternative method, (Cesari, L.; Kannan, R.; Schuur, J., Nonlinear Functional Analysis and Differential Equations (1976), Dekker: Dekker New York), 1-197 · Zbl 0343.47038 [3] Nagle, K., Nonlinear boundary value problems for ordinary differential equations with a small parameter, SIAM J. math. Analysis, 9, 719-729 (1978) · Zbl 0389.34017 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.