POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

Faouzi Haddouchi, Slimane Benaicha
unpublished
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation u (t) + λa(t)f (u(t)) = 0, 0 < t < 1, u (0) = 0, u(1) = α η 0 u(s)ds, where λ > 0 is a parameter, 0 < η < 1, 0 < α < 1 η. By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for
more » ... ient conditions for the existence of at least one positive solutions are established. Mathematics Subject Classification (2010): 34B15, 34C25, 34B18
fatcat:piydqh5y2beh5aci5io64xiiem