Abstract
We discuss positive solutions of integral equations for problems that arise from nonlinear boundary value problems. The boundary conditions can be either of local or nonlocal type. We concentrate on the case where the nonlinear term f(t,u) depends explicitly on t and this dependence is crucial. We give new fixed-point index results using a comparison theorem for a class of linear operators related to the u 0-positive operators of Krasnosel’skiĭ. These are used to establish new results on existence and nonexistence of positive solutions under some conditions which can be sharp.
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