DEPENDENCE RESULTS ON ALMOST PERIODIC AND ALMOST AUTOMORPHIC SOLUTIONS OF EVOLUTION EQUATIONS

作者：Blot Joel^*; Cieutat Philippe; N'Guerekata Gaston M

来源：Electronic Journal of Differential Equations, 2010, 101.

• Semilinear evolution equation
• almost periodic function
• almost automorphic function
• dependence results

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.

• 出版日期2010-7-21