Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic bounda...Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem （-△）mu=a1（x）uα1＋a2（x）uα2 , lim｜x｜→1 u（x） （1-｜x｜）m-1 =0, where α1,α2∈（-1, 1） and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.展开更多
文摘Let m be a positive integer and B be the unit ball of Rn （n≥2）. We investigate the existence, uniqueness and the asymptotic behavior of a positive continuous solution to the following semilinear polyharmonic boundary value problem （-△）mu=a1（x）uα1＋a2（x）uα2 , lim｜x｜→1 u（x） （1-｜x｜）m-1 =0, where α1,α2∈（-1, 1） and a1, a2 are two nonnegative measurable functions on B satisfying some appropriate assumptions related to Karamata regular variation theory.
