Guo, Dajun; Lakshmikantham, V. Multiple solutions of two-point boundary value problems of ordinary differential equations in Banach spaces. (English) Zbl 0645.34014 J. Math. Anal. Appl. 129, No. 1, 211-222 (1988). This paper deals with the existence of multiple positive solutions of the boundary value problem \(-x''=f(t,x)\), \(t\in I\), \(x(0)=x(1)=\theta\), where \(I=<0,1>\) and f is a continuous mapping from \(I\times P\) into P (P is a normal cone of the real Banach space E) and \(\theta\) is the zero element of E. Some special cases are discussed. Reviewer: P.Chocholatý Cited in 1 ReviewCited in 41 Documents MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:multiple positive solutions PDFBibTeX XMLCite \textit{D. Guo} and \textit{V. Lakshmikantham}, J. Math. Anal. Appl. 129, No. 1, 211--222 (1988; Zbl 0645.34014) Full Text: DOI References: [1] Lakshmikantham, V.; Leela, S., Nonlinear Differential Equations in Abstract Spaces (1981), Pergamon: Pergamon Oxford · Zbl 0456.34002 [2] Deimlling, K., Ordinary Differential Equations in Banach Spaces (1977), Springer-Verlag: Springer-Verlag Berlin [3] Guo, Dajun, Positive solutions of nonlinear operator equations and its applications to nonlinear integral equations, Adv. in Math., 13, 294-310 (1984), [In Chinese] · Zbl 0571.47044 [4] Potter, A. J.B., A fixed point theorem for positive \(k\)-set contractions, (Proc. Edinburgh Math. Soc., 19 (1974)), 93-102, (2) · Zbl 0275.47039 [5] Cac, N. P.; Gatica, J. A., Fixed point theorems for mappings in ordered Banach spaces, J. Math. Anal. Appl., 71, 547-557 (1979) · Zbl 0448.47035 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.