EXISTENCE OF SOLUTIONS FOR SUBLINEAR EQUATIONS ON EXTERIOR DOMAINS

In this article we prove the existence of an infinite number of radial solutions of Delta u+K(r)f(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, B-R, centered at the origin in R-N with u = 0 on partial derivative B-R and lim(r ->infinity) u(r) = 0 where N > 2, f is odd with f < 0 on (0, beta), f > 0 on (beta, infinity), f(u) similar to u(p) with 0 < p < 1 for large u and K(r) similar to r(-alpha) with 0 < alpha < 2 for large r.