He, Yanqin; Han, Xiaoling The existence and uniqueness of positive solutions for a class of third-order boundary value problems with integral boundary conditions. (Chinese. English summary) Zbl 1463.34096 J. Sichuan Univ., Nat. Sci. Ed. 57, No. 5, 852-856 (2020). Summary: In this paper, by using the mixed monotone operator method, we study the existence and uniqueness of positive solutions for the following third-order ordinary differential equations with integral boundary conditions: \[ \begin{cases} -u'''(t) = f(t,u(t),u(\xi t)) + g(t,u(t)),\; t \in (0,1), \xi \in (0,1), \\ u(0) = u''(0) = 0,\; u'(1) = \int_0^1 q(t)u'(t){\mathrm{d}}t, \end{cases} \] where \(f:[0,1] \times [0, +\infty)^2 \to [0, \infty)\) is continuous, \(g:[0,1] \times [0, \infty) \to [0, \infty)\) is continuous, \(q \in C([0,1], [0, +\infty))\). Cited in 1 Document 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:third-order boundary value problem; integral boundary condition; positive solution; existence and uniqueness; mixed monotone operator PDFBibTeX XMLCite \textit{Y. He} and \textit{X. Han}, J. Sichuan Univ., Nat. Sci. Ed. 57, No. 5, 852--856 (2020; Zbl 1463.34096) Full Text: DOI