Some existence results of positive solution to second-order boundary value problems
Summary: We study the existence of positive and monotone solution to the boundary value problem \(u''(t) + f(t, u(t)) = 0\), \(0 \leqslant t \leqslant 1\), \(u(0) = \xi u(1)\), \(u'(1) = \eta u'(0)\), where \(\xi, \eta \in(0,1) \cup(1, \infty)\). The main tool is the fixed point theorem of cone expansion and compression of functional type by \textit{R. Avery} et al. [Electron. J. Differ. Equ. 2008, Paper No. 22, 12 p. (2008; Zbl 1149.47042)]. Finally, four examples are provided to demonstrate the availability of our main results.
scientific article; zbMATH DE number 7022533
scientific article