Toshiki Naito

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For A(t) and f (t, x, y) T-periodic in t, we consider the following evolution equation with infinite delay in a general Banach space X: u (t) + A(t)u(t) = f t, u(t), u t , t >0, u(s) = φ(s), s 0, (0.1) where the resolvent of the unbounded operator A(t) is compact, and u t (s) = u(t + s), s 0. By utilizing a recent asymptotic fixed point theorem of Hale and(More)
We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form _ x = A(t)x+f(t) (), with f having precompact range, which will be then applied to nd new spectral criteria for the existence of almost periodic solutions with speciic spectral properties in the resonnant case where e(More)
This paper is concerned with a general existence and continuous dependence of mild solutions to semilinear functional differential equations with infinite delay in Banach spaces. In particular, our results are applicable to the equations whose Co-semigroups and nonlinear operators, defined on an open set, are noncompact. Introduction. Let £ be a Banach(More)
This paper is concerned with equations of the form: u = A(t)u + f (t) , where A(t) is (unbounded) periodic linear operator and f is almost periodic. We extend a central result on the spectral criteria for almost periodicity of solutions of evolution equations to some classes of periodic equations which says that if u is a bounded uniformly continuous mild(More)
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