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Periodic trajectories for evolution equations in Banach spaces. (English) Zbl 1095.47054

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.

MSC:

47J35 Nonlinear evolution equations
34C25 Periodic solutions to ordinary differential equations
35K55 Nonlinear parabolic equations
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