Copyright © 2009 Irena Rachůnková et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We discuss the properties of the differential equation , a.e. on ,
where , and satisfies the -Carathéodory conditions on for some . A full description of the asymptotic behavior for of functions satisfying the equation a.e. on is
given. We also describe the structure of boundary conditions which
are necessary and sufficient for to be at least in . As an application of the theory, new existence and/or uniqueness
results for solutions of periodic boundary value problems are