Existence and uniqueness results for the integro-differential equation
subject to the boundary condition
and, especially, for the linear case are given. To this end, this equation is written as operator equation in a suitable Hölder space. The main tools are the calculation of the spectral radius in the linear case, and fixed point principles in the nonlinear case.
Cite this article
W. Kohl, On a Class of Parabolic Integro-Differential Equations. Z. Anal. Anwend. 19 (2000), no. 1, pp. 159–201DOI 10.4171/ZAA/945