Han, Xiaoling Positive solutions for a three-point boundary value problem at resonance. (English) Zbl 1125.34014 J. Math. Anal. Appl. 336, No. 1, 556-568 (2007). Summary: This paper deals with the second-order three-point boundary value problem \[ x''(t)=f(t,x(t)),\quad t\in(0,1), \]\[ x'(0)=0,\quad x(\eta)= x(1). \] The existence and multiplicity of positive solutions are investigated by means of the fixed point theorem in cones. Cited in 33 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations Keywords:three-point boundary value problem; fixed point theorem; positive solution; resonance PDFBibTeX XMLCite \textit{X. Han}, J. Math. Anal. Appl. 336, No. 1, 556--568 (2007; Zbl 1125.34014) Full Text: DOI References: [1] Il’in, V.; Moiseev, E., Non-local boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, Differ. Equ., 23, 803-810 (1987) · Zbl 0668.34025 [2] Gupta, C., Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation, J. Math. Anal. Appl., 168, 540-551 (1992) · Zbl 0763.34009 [3] Zhang, G.; Sun, J., Positive solutions of \(m\)-point boundary value problems, J. Math. Anal. Appl., 291, 406-418 (2004) · Zbl 1069.34037 [4] Wei, Z.; Pang, C., Positive solutions of some singular \(m\)-point boundary value problems at non-resonance, Appl. Math. Comput., 171, 433-449 (2005) · Zbl 1085.34017 [5] Zhang, G.; Sun, J., Multiple positive solutions of singular second-order \(m\)-point boundary value problems, J. Math. Anal. Appl., 317, 442-447 (2006) · Zbl 1094.34017 [6] Karakostas, G.; Tsamatos, P., On a nonlocal boundary value problem, J. Math. Anal. Appl., 259, 209-218 (2001) · Zbl 1002.34057 [7] Ma, R., Positive solutions of a nonlinear three-point boundary value problem, Electron. J. Differential Equations, 34, 1-8 (1999) [8] Webb, J., Positive solutions of some three point boundary value problems via fixed point index theory, Nonlinear Anal., 47, 4319-4332 (2001) · Zbl 1042.34527 [9] Ma, R., Existence results of a \(m\)-point boundary value problem at resonance, J. Math. Anal. Appl., 294, 147-157 (2004) · Zbl 1070.34028 [10] Feng, W.; Webb, J., Solvability of a \(m\)-point boundary value problems at resonance, Nonlinear Anal., 30, 3227-3238 (1997) · Zbl 0891.34019 [11] Gupta, C., Solvability of a multi-point boundary value problem at resonance, Results Math., 28, 270-276 (1995) · Zbl 0843.34023 [12] Gupta, C., Existence theorems for a second order \(m\)-point boundary value problems at resonance, Int. J. Math. Math. Sci., 18, 705-710 (1995) · Zbl 0839.34027 [13] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press: Academic Press New York · Zbl 0661.47045 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.