Periodic solutions to nonlinear equations with oblique boundary conditions

We study the existence of positive periodic solutions to nonlinear elliptic and parabolic equations with oblique and dynamical boundary conditions and non-local terms. The results are obtained through fixed point theory, topological degree methods and properties of related linear elliptic problems with natural boundary conditions and possibly nonsymmetric principal part. As immediate consequences, we also obtain estimates on the principal eigenvalue for non-symmetric elliptic eigenvalue problems. © 2012 Juliusz Schauder University Centre for Nonlinear Studies.