Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems

For the nth order nonlinear differential equation y⁽ⁿ⁾(t)=f(y(t)), t [0,1], satisfying the multipoint conjugate boundary conditions, y^(j)(a_i) = 0,1 i k, 0 j n_i - 1, 0 =a₁ < a₂ < < a_k = 1, and _i=1^kn_i=n, where f: [0, ) is continuous, growth condtions are imposed on f which yield the existence of at least three solutions that belong to a cone.