EXISTENCE OF TRAVELING WAVE-FRONT SOLUTIONS FOR THE DISCRETE NAGUMO EQUATION

In this paper we show that the discrete Nagumo equation n = d(un -1 +2un + n + 1)+f(un), n εZ has a traveling wave solution for sufficiently strong coupling d. The problem is at first simplified into a fixed point problem which can be solved by Brouwer's fixed point theorem. The solutions of the simplified problem are then continued via index-theory to solutions of approximate problems. In the final step it is proven that the solutions of the approximate problems have a limit point which corresponds to a solution of the original problem. © 1992.