Combined effects in a semilinear polyharmonic problem in the unit ball

Let m be a positive integer and B be the unit ball of ℝ(n ≥ 2). We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem (−Δ)m u=a1(x)uα1+a2(x)uα2,|x|→1limu(x)(1−|x|)m−1=0,where α1},α_2∈(-1,1) and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.