Resonance problems for some non-autonomous ordinary differential equations

Recent years have seen a lot of activity in the study of quasilinear non-autonomous ordinary differential equations or systems of the form. where is some homeomorphism such that between the open sets A and B. The situation generalizes the classical case where is the identity, and the well-studied case of the p-Laplacian. where Contemporary researches concern less standard situations where (singular homeomorphism) and (bounded homeomorphism), where is the open ball of centre and radius. For model for the first case, namely corresponds to acceleration in special relativity, and a model for the second situation, namely corresponds to problem with curvature satisfying various conditions. In those case, both topological and variational methods, and sometimes combination of themgive new complementary existence and multiplicity results. We will describe some of them. Some attention will be given to the generalized forced pendulum equation. when is singular or bounded. ©Springer-Verlag Berlin Heidelberg 2013.