Abstract
Let m be a positive integer. We investigate the existence and the asymptotic behavior of positive continuous solutions to the following semilinear polyharmonic boundary value problem in the unit ball B of R-n (n >= 2):
(-Delta)(m) u = a(x)u(alpha), lim(|x|-> 1) u(x)/(1 - |x|)(m-1) = 0,
where -1 < alpha < 1 and a is a positive measurable function in B such that there exists c > 0 satisfying for each x is an element of B,
1/c <= a(x)(1 - |x|)(lambda) exp (-integral(eta)(1-|x|) z(s)/sds) <= c,
eta > 1, lambda <= m(1 + alpha) + 1 - alpha and z is a continuous function on [0, eta] with z(0) = 0. (C) 2011 Elsevier Ltd. All rights reserved.