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Zbl 0998.45004
Karakostas, G.L.; Tsamatos, P.Ch.
Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems. (English)
[J] Electron. J. Differ. Equ. 2002, Paper No.30, 17 p., electronic only (2002). ISSN 1072-6691/e

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.
[P.B.Dubovski (Moskva)]

MSC 2000:: *45M20 Positive solutions of integral equations
34B18 Positive solutions of nonlinear boundary value problems
45G10 Nonsingular nonlinear integral equations

Keywords: semilinear ordinary differential equation; nonlinear Fredholm integral equation; Krasnoselskii fixed point theorem; multiplicity of solutions; positive solutions; existence; cone

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