ON SOLUTIONS OF THE NONHOMOGENEOUS CAUCHY PROBLEM FOR PARABOLIC TYPE DIFFERENTIAL EQUATIONS IN A BANACH SPACE

For a differential equation of the form $u'(t) + Au(t) = f(t), t \in (0,\infty)$, where $A$ is infinitesimal generator bounded analytic $C_{0}$-semigroup linear operators in Banach space $\mathfrak{B}, \ f(t)$ $\mathfrak{B}$-valued polynomial, behavior preassigned points solutions Cauchy problem $u(0) u_{0} \mathfrak{B}$ depending on $f(t)$ investigated.