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Multiple solutions of two-point boundary value problems of ordinary differential equations in Banach spaces. (English) Zbl 0645.34014

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

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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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
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