Abstract

In this paper we will study the problem of existence of positive solutions to the problem (D) {((a (r) f{symbol} (u'))' + b (r) g (u) = 0, a.e. in (0, R),; under(lim, r ? 0) a (r) f{symbol} (u' (r)) = 0, u (R) = 0,) where f{symbol} is an odd increasing homeomorphism of R and g ? C (R) is such that g (z) > 0 for all z > 0 with g (0) = 0. The functions a and b, that we will refer to as weight functions, satisfy a (r) > 0, b (r) > 0 for all r ? (0, R] and are such that a, b ? C1 (0, R] n L1 (0, R). If f{symbol} has the form f{symbol} (z) = z m (| z |), and a (r) = rN - 1 over(a, ~) (r), b (r) = rN - 1 over(b, ~) (r), N = 2, then solutions of problem (D) provide solutions with radial symmetry for the problem (P) {(div (over(a, ~) (| x |) m (| ? u |) ? u) + over(b, ~) (| x |) g (u) = 0, x ? O, u = 0, x ? ? O,) where O = B (0, R) denotes the ball with center 0 and radius R > 0 in RN. © 2008 Elsevier Ltd. All rights reserved.