Infante, Gennaro Nonlocal boundary value problems with two nonlinear boundary conditions. (English) Zbl 1198.34025 Commun. Appl. Anal. 12, No. 3, 279-288 (2008). Existence of positive solutions of the second order differential equation \[ u'' + g(t) f(t,u) =0 \]under the nonlinear boundary conditions\[ u'(0) +H_1(\alpha[u])=0, \, \sigma u'(1)+u(\eta)=H_2(\beta[u]) \]is established by the fixed point index theory for compact maps. Here, \(H_1\) and \(H_2:[0,\infty)\to [0,\infty)\) are continuous functions between two linear functions and\[ \alpha[u]= \int_0^1 u(s)\, DA(s),\qquad \beta[u] = \int_0^1 u(s)\, DB(s) \]are Lebesgue-Stieltjes integrals. Reviewer: Pablo Amster (Buenos Aires) Cited in 39 Documents MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 47H10 Fixed-point theorems Keywords:nonlocal boundary value problems; nonlinear boundary conditions; fixed point index PDFBibTeX XMLCite \textit{G. Infante}, Commun. Appl. Anal. 12, No. 3, 279--288 (2008; Zbl 1198.34025)