Solvability of an Initial–Boundary Value Problem for a Parabolic Equation with a Time-Nonlocal Term in Hölder spaces

We consider an initial–boundary value problem for a semilinear parabolic differentialequation with a time-nonlocal term. This term contains the integral of the solution over the entiretime interval on which the problem is considered. The solvability of the problem inHölder classes is proved. The uniqueness of the solution is established under a constrainton the length of the time interval over which the solution is integrated in the nonlocal term.