A new approach for the existence of time periodic solutions of special classes of nonlinear problems

We study the existence of one or more weak periodic solutions of nonlinear evolution PDEs in a cylinder of RN+1 with conditions on lateral surface by using the results connected to a general evolution variational equation depending on a parameter. To this aim we state existence theorems and in some particular cases we give sufficient conditions about the nonstationarity of the found solutions. In these nonlinear evolution PDEs second partial derivatives with respect to time are also present.