A study on controllability of semilinear integrodifferential systems in Banach spaces
The authors established the sufficient conditions for controllability of the following semilinear integrodifferential systems in a Banach space: \[ \begin{gathered}{d\over dt} [x(t)+ g(t, x(t))]= Ax(t)+ (Bu)(t)+ f(t, x(t)),\\ \int^t_0 h(t, s,x(s))\,ds,\quad t\in J= [0,b],\qquad x(0)= x_0,\end{gathered} \] where the state \(x(\cdot)\) takes values in a Banach space \(X\) with the norm \(\|\cdot\|\) and the control function \(u(\cdot)\) is given in \(L^2(J,U)\), a Banach space of admissible control functions with \(U\) as a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.
scientific article; zbMATH DE number 2142323
scientific article