Zhao, Zhongzi; Ma, Ruyun Existence of positive solutions for a class of fourth-order ordinary differential equations with nonlinear boundary value. (Chinese. English summary) Zbl 1463.34114 J. Sichuan Univ., Nat. Sci. Ed. 57, No. 2, 236-242 (2020). Summary: We study the existence of positive solutions for a class of fourth-order ordinary differential equations with nonlinear boundary value \(u'''' = rf(t, u (t)), 0 < t < 1\), \(u (0) = u' (0) = u' (1) = u''' (1) + \varphi (u (1)) = 0\), where \(r\) is a positive parameter, \(\varphi (s) = sc (s), c \in C ([0, \infty), [0, 12) \cup (12, \infty))\). When \(u \to {0^+}\), \(f(t, u) = au + o (u)\), \(\varphi (s) = {a_1}s + o (s)\). When \(u \to \infty\), \(f(t, u) = bu + o (u)\), \(\varphi (s) = {b_1}s + o (s)\). The proof of the main results is based on the Dancer global bifurcation technique. MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B09 Boundary eigenvalue problems for ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations Keywords:nonlinear boundary condition; bifurcation method; positive solution PDFBibTeX XMLCite \textit{Z. Zhao} and \textit{R. Ma}, J. Sichuan Univ., Nat. Sci. Ed. 57, No. 2, 236--242 (2020; Zbl 1463.34114) Full Text: DOI