On \(C^\alpha\)-Hölder classical solutions for non-autonomous neutral differential equations: the nonlinear case (Q401124)

The authors study abstract neutral differential equations using the maximal regularity type technique for parabolic problems. This type of abstract neutral differential equations arise in the theory of heat conduction in fading memory material or in the theory of population dynamics with the tendency of populations to migrate from high population density regions to regions with minor density. The main result of this work gives some hypotheses which ensure the existence of unique classical solution. The proof of this result is based on the contraction mapping principle.