On the Existence of Two Solutions of the Four-Point Problem

We have proved the existence of at least two different solutions to the equation u″ = ƒ(t, u, u′, s), where s ∈ R. The solutions fulfill four-point conditions u(a) = u(c), u(d) = u(b), where a < c ≤ d < b, a, b, c, d ∈ R.