NONLOCAL SYSTEMS OF BVPS WITH ASYMPTOTICALLY SUBLINEAR BOUNDARY CONDITIONS

In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions. By imposing only a condition of asymptotic sublinear growth on the nonlinear boundary func- tions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be represented as Lebesgue-Stieltjes integrals possessing signed Borel measures. Because we only suppose the sublinearity of the the nonlinear boundary functions at positive infinity, we also remove many of the restrictive growth assumptions found in other recent works on closely related problems. We conclude with a numerical example to explicate the consequences of our main result.