Xu, Xiaojie; Jiang, Daqing; O’Regan, Donal; Agarwal, R. P. Multiple positive solutions of fourth-order boundary value problems. (English) Zbl 1071.34025 Math. Inequal. Appl. 8, No. 1, 79-88 (2005). Summary: We discuss the existence of multiple positive solutions for the fourth-order boundary value problem \[ u^{(4)}(t)+\beta u''(t)= f(t, u(t)),\quad 0< t< 1,\quad u(0)= u(1)= u''(0)= u''(1)= 0, \] where \(f: [0,1]\times [0,\infty)\to [0,\infty)\) is continuous and \(\beta< \pi^2\). Existence is established via the theory of fixed-point index in cones. Cited in 2 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:existence; multiple positive solutions; cone; fixed point index PDFBibTeX XMLCite \textit{X. Xu} et al., Math. Inequal. Appl. 8, No. 1, 79--88 (2005; Zbl 1071.34025) Full Text: DOI