Existence For An Elliptic System With Nonlinear Boundary Conditions Via Fixed Point Methods

JULIAN FERNANDEZ BONDER; ROSSI, JULIO DANIEL

ADVANCES IN DIFFERENTIAL EQUATIONS

Khayyam P.O. Box 429 Athens OH 45701

Año: 2001 vol. 6 p. 1 - 20

1079-9389

In this paper we prove the existence of nonnegative nontrivial solutions of the system ½ ¢u = u in ­; ¢v = v; with nonlinear coupling through the boundary given by ( @u @n = f(x; u; v) on @­; @v @n = g(x; u; v); under suitable assumptions on the nonlinear terms f and g. For the proof we use a fixed-point argument and the key ingredient is a Liouville type theorem for a system of Laplace equations with nonlinear coupling through the boundary of power type in the half space.