A one-dimensional Kirchhoff equation with generalized convolution coefficients

For q >= 1 we consider the one-dimensional Kirchhoff-type problem -A((a * (u')(q))(1))u ''(t) = lambda f(t,u(t)), t is an element of (0, 1), where a * (u')(q) represents a finite convolution, subject to right-focal boundary conditions. Because the nonlocal coefficient is phrased in terms of convolution the results of this paper can accommodate all manner of nonlocal coefficients, such as a fractional derivative coefficient of Caputo type. A nonstandard order cone together with a specially tailored open set is used to deduce existence of at least one positive solution for this problem via topological fixed point theory.