On Bounded Entire Solutions of Integro-Differential Equations

Abstract

The author considers two types of integro-differential equations: (a) Δu+f(x,u)+∫ R n p(x,y)g(u)dy=0 and (b) u t =Δu+f(x,t,u)+∫ R n q(x,t,y)g(u)dy=0 . Assuming the existence of upper and lower solutions, the author proves the existence of classical solutions of (a), (b) by the method of monotone iteration. The main portion of the paper is devoted to examples in which the author constructs upper and lower radial solutions by solving ordinary integro-differential equations. The title of this paper is misleading because there is no discussion regarding analyticity anywhere in the results.