Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems. (English) Zbl 0998.45004

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.


45M20 Positive solutions of integral equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
45G10 Other nonlinear integral equations
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