Existence of at least one positive solution to the nonlocal differential equation − M ( (a ∗ (g ∘ u) ) ′ (1) ) u (t) = λ f (t, u (t) ), 0 > t > 1, equation -M ( (a* (g u) ) ’ (1) ) u (t) = f (t, u (t) ), \;0>t>1, equation subject to the right-focal boundary data u (0) = 0 = u ′ (1) u (0) =0=u’ (1), is considered. Depending upon the choice of the kernel a a in the finite convolution, (a ∗ (g ∘ u) ) ′ (1) (a* (g u) ) ’ (1), this formulation includes as a special case the Riemann–Liouville fractional derivative. Topological fixed point theory, carried out via a specialized order cone, is employed to deduce the main result. Due to the presence of the derivative in the nonlocal coefficient, we use a nonstandard index theory applicable to unbounded sets.
Christopher GOODRICH (Fri,) studied this question.