Vitali Vougalter, Vitaly Volpert
Solvability of some integro-differential equations with the double scale 
anomalous diffusion in higher dimensions 
(193K, pdf)

ABSTRACT.  The article is devoted to the studies of the existence of solutions of an integro-differential equation in the case of the double scale anomalous diffusion with the sum of the two negative Laplacians raised to two distinct fractional powers in R^d, d=4, 5. The proof of the existence of 
solutions is based on a fixed point technique. Solvability conditions for the non-Fredholm elliptic operators in unbounded domains are used.