  By means of topological methods, we provide new results on the existence,
non-existence, localization and multiplicity of nontrivial solutions for
systems of perturbed Hammerstein integral equations. In order to illustrate our
theoretical results, we study some problems that occur in applied mathematics,
namely models of chemical reactors, beams and thermostats. We also apply our
theory in order to prove the existence of nontrivial radial solutions of
systems of elliptic boundary value problems subject to nonlocal, nonlinear
boundary conditions.
