Voisei, Mircea D. Periodic trajectories for evolution equations in Banach spaces. (English) Zbl 1095.47054 Electron. J. Differ. Equ. 2005, Paper No. 103, 8 p. (2005). The author, by using the Leray–Schauder topological degree, proves the existence of a mild periodic solution in a general Banach space of the nonlinear evolution inclusion \[ y'(t)+Ay(t)\ni F(t,y(t)), \quad 0\leq t\leq T, \] where \(A\) is \(m\)-accretive such that \(-A\) generates a compact semigroup, and \(F\) is a Carathéodory mapping. Two examples concerning nonlinear evolution equations of parabolic type are also presented. Reviewer: Sotiris K. Ntouyas (Ioannina) MSC: 47J35 Nonlinear evolution equations 34C25 Periodic solutions to ordinary differential equations 35K55 Nonlinear parabolic equations Keywords:periodic solution; evolution equation of parabolic type PDFBibTeX XMLCite \textit{M. D. Voisei}, Electron. J. Differ. Equ. 2005, Paper No. 103, 8 p. (2005; Zbl 1095.47054) Full Text: EuDML EMIS