Nonlocal differential equations with convex convolution coefficients

We consider the nonlocal differential equation -A((b*(g omicron u))(1))u" (t) = lambda f(t,u(t)), ot<1 subject to a large class of boundary conditions. We demonstrate that such boundary value problems will admit at least one positive solution under, principally, an assumption that the function g is an increasing, continuous, and convex function. Because the nonlocal element is realized in a convolution form, a variety of nonlocalities are supported by the results, including fractional integrals of Riemann-Liouville type.