An application of a nonstandard cone to discrete boundary value problems with unbounded indefinite forcing

We consider the summation equation y(t) = gamma(t)H (Sigma(n)(i=1) alpha(i)y(xi(i))) + lambda Sigma(b)(s=0) G(t,s)f(s,y(s+1)) in the setting in which f may change sign. In fact, by means of the nonlocal element in the above summation equation, we are able to guarantee existence of at least one positive solution even in the case where for each and, furthermore, where . We obtain this result by applying a nonstandard order cone and attendant open set. Finally, by choosing the maps gamma and G in particular ways, we are able to relate positive solutions of the summation equation to positive solutions of discrete boundary value problems.