EXISTENCE OF INFINITELY MANY SOLUTIONS FOR SEMILINEAR PROBLEMS ON EXTERIOR DOMAINS

In this paper we prove the existence of infinitely many radial solutions of Delta u + K (r) f (u) = 0 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 superlinear for large u and 0 < K(r) <= K-1/r(alpha) with 2 < alpha < 2(N - 1) for large r.