COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL  

作　　者：Zagharide Zine EL ABIDINE 

机构地区：[1]Dpartement de Mathmatiques, Facult des Sciences de Tunis,Campus Universitaire,2092 Tunis, Tunisia

出　　处：《Acta Mathematica Scientia》2014年第5期1404-1416,共13页数学物理学报（B辑英文版）

摘　　要：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.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.

关 键 词：Kato class positive solution nonlinear polyharmonic equation ASYMPTOTICBEHAVIOR schauder fixed point theorem 

分 类 号：O174.2[理学—数学]