Gupta, Chaitan P.; Ntouyas, S. K.; Tsamatos, P. Ch. On an \(m\)-point-boundary-value problem for second-order ordinary differential equations. (English) Zbl 0815.34012 Nonlinear Anal., Theory Methods Appl. 23, No. 11, 1427-1436 (1994). An \(m\)-point boundary value problem of the form \(x'' = f(t,x,x')\), \(x(0) = 0\), \(x(1) = \sum^{m-2}_{i=1} a_ ix(\xi_ i)\) with \((t,x) \in [0,1] \times R\) is studied. Using the Leray-Schauder continuation theorem and the Wirtinger type inequality, the authors give conditions for the existence and uniqueness of a solution for this BVP. Theorems of the paper extend some recent results of the first author [J. Math. Anal. Appl. 186, 277-281 (1994; Zbl 0805.34017)]. Reviewer: M.G.Filippov (Kiev) Cited in 1 ReviewCited in 46 Documents MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations Keywords:\(m\)-point boundary value problem; Leray-Schauder continuation theorem; Wirtinger type inequality Citations:Zbl 0805.34017 PDFBibTeX XMLCite \textit{C. P. Gupta} et al., Nonlinear Anal., Theory Methods Appl. 23, No. 11, 1427--1436 (1994; Zbl 0815.34012) Full Text: DOI References: [1] Il’in, V. A.; Moiseev, E. I., Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, Diff. Eqns, 23, 27, 803-810 (1988) · Zbl 0668.34025 [2] Mawhin, J., Topological degree methods in nonlinear boundary value problems, (NSF-CBMS Regional Conference Series in Math. (1979), American Mathematical Society: American Mathematical Society Providence, RI), No. 40 · Zbl 0414.34025 [3] GUPTA C.P., A note on a second order three-point boundary value problem, J. math. Analysis Applic; GUPTA C.P., A note on a second order three-point boundary value problem, J. math. Analysis Applic · Zbl 0805.34017 [4] Gupta, C. P., Solvability of a three-point boundary value problem for a second order ordinary differential equation, J. math. Analysis Applic., 168, 540-551 (1992) · Zbl 0763.34009 [5] MARANO S.A., A remark on a second order three-point boundary value problem, J. math. Analysis Applic; MARANO S.A., A remark on a second order three-point boundary value problem, J. math. Analysis Applic · Zbl 0801.34025 [6] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities (1967), Cambridge University Press: Cambridge University Press London · Zbl 0634.26008 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.