Karakostas, G. L.; Tsamatos, P. Ch. Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems. (English) Zbl 0998.45004 Electron. J. Differ. Equ. 2002, Paper No. 30, 17 p. (2002). The authors establish a connection between second order semilinear ordinary differential equations with linear integral boundary conditions and nonlinear Fredholm integral equations. Under certain positivity and concavity conditions the authors apply the Krasnoselskii fixed point theorem to prove the existence result in a suitable cone. Moreover, the authors select the cases when the equation has two or three solutions. The hypotheses on the functions seem rather restrictive but the authors provide no example when such conditions can meet. Reviewer: P.B.Dubovski (Moskva) Cited in 100 Documents MSC: 45M20 Positive solutions of integral equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 45G10 Other nonlinear integral equations Keywords:semilinear ordinary differential equation; nonlinear Fredholm integral equation; Krasnoselskii fixed point theorem; multiplicity of solutions; positive solutions; existence; cone PDFBibTeX XMLCite \textit{G. L. Karakostas} and \textit{P. Ch. Tsamatos}, Electron. J. Differ. Equ. 2002, Paper No. 30, 17 p. (2002; Zbl 0998.45004) Full Text: EuDML EMIS