Zhai, Chengbo; Jiang, Chunrong Existence and uniqueness of convex monotone positive solutions for boundary value problems of an elastic beam equation with a parameter. (English) Zbl 1349.34090 Electron. J. Qual. Theory Differ. Equ. 2015, Paper No. 81, 11 p. (2015). Summary: The purpose of this paper is to investigate the existence and uniqueness of convex monotone positive solutions for a boundary value problem of an elastic beam equation with a parameter. The proofs of the main results rely on a fixed point theorem and some properties of eigenvalue problems for a class of general mixed monotone operators. The results can guarantee the existence of a unique convex monotone positive solution and can be applied to construct two iterative sequences for approximating it. Moreover, we present some properties of convex monotone positive solutions for the boundary value problem dependent on the parameter. Finally, an example is given to illustrate the main results. Cited in 4 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 34B09 Boundary eigenvalue problems for ordinary differential equations Keywords:existence and uniqueness; convex monotone positive solution; elastic beam equation; fixed point theorem for mixed monotone operators PDFBibTeX XMLCite \textit{C. Zhai} and \textit{C. Jiang}, Electron. J. Qual. Theory Differ. Equ. 2015, Paper No. 81, 11 p. (2015; Zbl 1349.34090) Full Text: DOI