Triple positive solutions of three-point boundary value problems for fourth-order differential equations

摘要

Using the Avery and Peterson fixed point theorem, we investigate the existence of three positive solutions for the fourth order three-point boundary value problem u~((4))(t) = h(t)f(t, u(t), u"(t)), 0 < t < 1, u(0) = u(l) = 0, c_1u"(ξ) - c_2u"'(ξ) = 0, cξu"(1) + c_4u'"(l) = 0, where c_1, C_2.C_3 and c_4 arenonnegativeconstants satisfying c_1c_4+c_2 c_3+c_1c_3 > 0,0 < ξ < 1 and h(t) is sign-changing on |0,1]. The interesting point is that the nonlinear term is allowed to depend on u".