Sun, Yongping; Liu, Lishan Solvability for a nonlinear second-order three-point boundary value problem. (English) Zbl 1069.34018 J. Math. Anal. Appl. 296, No. 1, 265-275 (2004). Using the Leray-Schauder nonlinear alternative theory, a nonconstant solution is found under suitable new conditions for the following three-point BVP \[ u'' +f(t,u)=0,\quad 0<t<1, \quad u'(0)=0, u(1)=\alpha u(\eta), \] with \(0<\eta<1\) and \(\alpha>0\) or \(\alpha<0\). Some examples are given to illustrate the results. Reviewer: Yujun Dong (Nanjing) Cited in 29 Documents MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:second-order nonlinear ordinary differential equation; three point boundary value problem; Leray-Schauder nonlinear alternative PDFBibTeX XMLCite \textit{Y. Sun} and \textit{L. Liu}, J. Math. Anal. Appl. 296, No. 1, 265--275 (2004; Zbl 1069.34018) Full Text: DOI References: [1] Deimling, K., Nonlinear Functional Analysis (1985), Springer: Springer Berlin · Zbl 0559.47040 [2] Feng, W.; Webb, J. R.L, Solvability of three-point boundary value problem at resonance, Nonlinear Anal., 30, 3227-3238 (1997) · Zbl 0891.34019 [3] Gupta, C. P., Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations, J. Math. Anal. Appl., 168, 540-551 (1992) · Zbl 0763.34009 [4] Gupta, C. P., Solvability of an \(m\)-point nonlinear boundary value problem for second order ordinary differential equations, J. Math. Anal. Appl., 189, 575-584 (1995) · Zbl 0819.34012 [5] Gupta, C. P., A shaper condition for the solvability of a three-point second order boundary value problem, J. Math. Anal. Appl., 205, 586-597 (1997) · Zbl 0874.34014 [6] Liu, B., Positive solutions of a nonlinear three-point boundary value problem, Comput. Math. Appl., 44, 201-211 (2002) · Zbl 1008.34014 [7] Liu, B., Positive solutions of a nonlinear three-point boundary value problem, Appl. Math. Comput., 132, 11-28 (2002) · Zbl 1032.34020 [8] Ma, R., Existence theorems for second order three-point boundary value problems, J. Math. Anal. Appl., 212, 545-555 (1997) · Zbl 0884.34024 [9] Ma, R., Positive solutions of a nonlinear three-point boundary value problems, Electron. J. Differential Equations, 34, 1-8 (1999) [10] Ma, R., Multiplicity results for three-point boundary value problem at resonance, Nonlinear Anal., 53, 777-789 (2003) · Zbl 1037.34011 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.