Nonlinear BVPS with functional parameters

We study the existence, nonexistence and properties of solutions for a certain class of second-order ODEs and their dependence on functional parameters, also in the case when nonlinearities are, in some sense, singular. This approach is based on variational methods and cover both sublinear and superlinear cases. We develop a duality theory and variational principles for this problem. As a consequence of the duality theory we give a numerical version of the variational principle which enables approximation of the solution for our problem. We apply these results to obtain the existence of bounded, radial and positive classical solutions for the BVP of elliptic type. Observe that our method allows us to investigate a certain class of elliptic systems in both bounded annular domain and exterior domain.