He, Yanqin; Han, Xiaoling Monotone positive solutions of fourth-order boundary value problems with integral boundary conditions. (Chinese. English summary) Zbl 1449.34074 J. Shandong Univ., Nat. Sci. 54, No. 12, 32-37 (2019). Summary: By using the monotone iterative technique, this article studies the existence of monotone positive solutions for fourth order boundary value problems with integral boundary conditions \[\begin{cases} u^{ (4)} (t) = f (t,u (t), u' (t)),\; t \in (0,1),\\ u (0) = u' (1) = u''' (1) = 0,\\ u'' (0) = \int_0^1 g (t)u'' (t){\mathrm{d}}t, \end{cases}\] where \(f:[0,1] \times [0,+\infty)^2 \to [0,+\infty)\) is continuous. MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations Keywords:fourth-order boundary value problem; integral boundary condition; monotone positive solution; iterative technique PDFBibTeX XMLCite \textit{Y. He} and \textit{X. Han}, J. Shandong Univ., Nat. Sci. 54, No. 12, 32--37 (2019; Zbl 1449.34074) Full Text: DOI