Su, Hua; Liu, Lishan; Wu, Yonghong Positive solutions for Sturm-Liouville boundary value problems in a Banach space. (English) Zbl 1251.34076 Abstr. Appl. Anal. 2012, Article ID 572172, 11 p. (2012). Summary: We consider the existence of single and multiple positive solutions for a second-order Sturm-Liouville boundary value problem in a Banach space. A sufficient condition for the existence of a positive solution is obtained by a fixed point theorem. Cited in 3 Documents MSC: 34G10 Linear differential equations in abstract spaces 34B24 Sturm-Liouville theory 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations Keywords:fixed point theorem PDF BibTeX XML Cite \textit{H. Su} et al., Abstr. Appl. Anal. 2012, Article ID 572172, 11 p. (2012; Zbl 1251.34076) Full Text: DOI References: [1] R. Dalmasso, “Positive solutions of singular boundary value problems,” Nonlinear Analysis, vol. 27, no. 6, pp. 645-652, 1996. · Zbl 0860.34008 [2] R. P. Agarwal and Y. M. Chow, “Iterative methods for a fourth order boundary value problem,” Journal of Computational and Applied Mathematics, vol. 10, no. 2, pp. 203-217, 1984. · Zbl 0541.65055 [3] Y. S. Choi, “A singular boundary value problem arising from near-ignition analysis of flame structure,” Differential and Integral Equations, vol. 4, no. 4, pp. 891-895, 1991. · Zbl 0795.34015 [4] D. O’Regan, “Solvability of some fourth (and higher) order singular boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 161, no. 1, pp. 78-116, 1991. · Zbl 0795.34018 [5] C. P. Gupta, “Existence and uniqueness results for the bending of an elastic beam equation at resonance,” Journal of Mathematical Analysis and Applications, vol. 135, no. 1, pp. 208-225, 1988. · Zbl 0655.73001 [6] Z. L. Wei, “Positive solutions of singular Dirichlet boundary value problems at nonresonance,” Chinese Annals of Mathematics. Series A, vol. 20, no. 5, pp. 543-552, 1999 (Chinese). · Zbl 0948.34501 [7] A. R. Aftabizadeh, “Existence and uniqueness theorems for fourth-order boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 116, no. 2, pp. 415-426, 1986. · Zbl 0634.34009 [8] Y. Liu and H. Yu, “Existence and uniqueness of positive solution for singular boundary value problem,” Computers & Mathematics with Applications, vol. 50, no. 1-2, pp. 133-143, 2005. · Zbl 1094.34015 [9] H. Li and Y. Liu, “On sign-changing solutions for a second-order integral boundary value problem,” Computers & Mathematics with Applications, vol. 62, no. 2, pp. 651-656, 2011. · Zbl 1228.34032 [10] H. Li and J. Sun, “Positive solutions of sublinear Sturm-Liouville problems with changing sign nonlinearity,” Computers & Mathematics with Applications, vol. 58, no. 9, pp. 1808-1815, 2009. · Zbl 1197.34040 [11] J. Yang, Z. Wei, and K. Liu, “Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems,” Applied Mathematics and Computation, vol. 214, no. 2, pp. 424-432, 2009. · Zbl 1215.34035 [12] H. Su, Z. Wei, and F. Xu, “The existence of positive solutions for nonlinear singular boundary value system with p-Laplacian,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 826-836, 2006. · Zbl 1111.34020 [13] D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988. · 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.