Dependence results on almost periodic and almost automorphic solutions of evolution equations

• Main Authors: Joel Blot, Philippe Cieutat, Gaston M. N'Guerekata
• Format: Article
• Language: English
• Published: Texas State University 2010-07-01
• Series: Electronic Journal of Differential Equations
• Subjects: Semilinear evolution equation; almost periodic function; almost automorphic function; dependence results
• Online Access: http://ejde.math.txstate.edu/Volumes/2010/101/abstr.html
• ISSN: 1072-6691

We consider the semilinear evolution equations $x'(t) = A(t) x(t) + f(x(t), u(t),t)$ and $x'(t) = A(t) x(t) + f(x(t), zeta,t)$ where $A(t)$ is a unbounded linear operator on a Banach space X and f is a nonlinear operator. We study the dependence of solutions x with respect to the function $u$ in three cases: the continuous almost periodic functions, the differentiable almost periodic functions, and the almost automorphic functions. We give results on the continuous dependence and on the differentiable dependence.