We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ i...We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.展开更多
In this work, we study the existence and uniqueness of pseudo almost periodic solutions for some difference equations. Firstly, we investigate the spectrum of the shift operator on the space of pseudo almost periodic ...In this work, we study the existence and uniqueness of pseudo almost periodic solutions for some difference equations. Firstly, we investigate the spectrum of the shift operator on the space of pseudo almost periodic sequences to show the main results of this work. For the illustration, some applications are provided for a second order differential equation with piecewise constant arguments.展开更多
文摘We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.
文摘In this work, we study the existence and uniqueness of pseudo almost periodic solutions for some difference equations. Firstly, we investigate the spectrum of the shift operator on the space of pseudo almost periodic sequences to show the main results of this work. For the illustration, some applications are provided for a second order differential equation with piecewise constant arguments.
