INFINITELY MANY SOLUTIONS FOR A SEMILINEAR PROBLEM ON EXTERIOR DOMAINS WITH NONLINEAR BOUNDARY CONDITION

In this article we prove the existence of an infinite number of radial solutions to Delta u+K(r) f(u)= 0 with a nonlinear boundary condition on the exterior of the ball of radius R centered at the origin in R-N such that lim(r ->infinity) u(r) = 0 with any given number of zeros where f : R -> R is odd and there exists a beta > 0 with f < 0 on (0,0), f > 0 on (beta,infinity) with f superlinear for large u, and K(r) similar to r(-alpha)with 0 < alpha < 2(N - 1).