GLOBAL C^(1,2)-SOLUTION TO FUNCTIONAL REACTION-DIFFUSION PROBLEM

This paper is concerned with the existence, uniqueness, comparison and dynamics problem of a functional reaction-diffusion problem. The existence and uniqueness of the global C1,2 strong solution to the problem is derived using Schauder fixed point theorem in Banach space instead of the Ascoli-Arzela theorem in the unbounded region, meanwhile, the maximal and minimal solutions are also presented by the monotone iteration method with a pair of supper and lower solutions as the initial iteration.

SECOND BOUNDARY VALUE PROBLEM FOR NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

In this paper we prove a uniqueness theorem of solutions for second boundary value problem of a class of second order nonlinear differential equation. In the proof the spectral theory of second order differential operators and Schauder's fixed point theorem are used.