SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS  

作　　者：张学梅 阚士坤 Xuemei ZHANG;Shikun KAN(School of Mathematics and Physics,North China Electric Power University,Beijing,102206,China)

机构地区：[1]School of Mathematics and Physics,North China Electric Power University,Beijing,102206,China

出　　处：《Acta Mathematica Scientia》2023年第3期1175-1194,共20页数学物理学报（B辑英文版）

基　　金：supported by the Beijing Natural Science Foundation(1212003)。

摘　　要：Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.

关 键 词：singular p-Laplacian equation boundary blow-up sub-supersolution method EXISTENCE nonexistence and estimates sufficient and necessary conditions 

分 类 号：O175.29[理学—数学]