Peano type theorem for abstract parabolic equations
Periodic solutions of degenerate differential equations in vector-valued function spaces
Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces.
Periodic systems dependent on parameters.
Problemi di trasmissione per sistemi parabolici nonlineari di tipo Phase-Field