Periodic Solutions for Nonlinear Evolution Equations in a Banach Space
نویسنده
چکیده
We prove an existence result for 7"-periodic mild solutions to nonlinear evolution equations of the form u(t) + Au(t) BF(t, u(t)) , t€R+. y Here (X, \\-\\) is a real Banach space, A: D(A) C X —> 2 is an operator with A — a! m-accretive for some a > 0 and such that -A. generates a compact semigroup, while F: R+ x D(A) —► X is a Carathéodory mapping which is T-periodic with respect to its first argument and satisfies ^Hm^suplllFU, v)\\ ; t£ R+,v eD(A), \\v\\ < r} < a. As a consequence, we obtain an existence theorem for T-periodic solutions to the porous medium equation.
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تاریخ انتشار 2010