Nonlocal differential equations with (p, q) growth

The author considers a class of nonlocal convolution-type ordinary differential equations of the form -??((?? & lowast; (g ? ??))(1))??''(??) = ????(??, ??(??)), 0 < ?? < 1where g is a continuous function satisfying (??, ??)growth & mdash; that is, there exist constants ??(1), ??(2)is an element of (0, infinity) and ??(3 )is an element of [0, infinity)such that ??(1)??(??) ? g(??) ? ??(2)(??(3 )+ ??(??)),?? ? 0,where 1 ? ?? ? ??< + infinity. Existence of at least one positive solution to this equation when subjected to given boundary data is studied by means of topological fixed point theory