POSITIVE LIOUVILLE THEOREMS AND ASYMPTOTIC BEHAVIOR FOR p-LAPLACIAN TYPE ELLIPTIC EQUATIONS WITH A FUCHSIAN POTENTIAL

Confluentes Mathematici

PINCHOVER, YEHUDA¹  FRAAS, MARTIN² 

[1] Department of Mathematics, Technion — Israel Institute of Technology, Haifa, 32000, Israel;Department of Physics, Technion — Israel Institute of Technology, Haifa, 32000, Israel

关键词: Fuchsian operator;    isolated singularity;    Liouville theorem;    p-Laplacian;    positive solutions;    quasilinear elliptic operator;    removable singularity;   

DOI  :  10.1142/S1793744211000321

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form -Δp(u) + V|u|p-2 u = 0 in X, where X is a domain in ℝd, d ≥ 2 and 1 < p < ∞. We assume that the potential V has a Fuchsian type singularity at a point ζ, where either ζ = ∞ and X is a truncated C2-cone, or ζ = 0 and ζ is either an isolated point of ∂X or belongs to a C2-portion of ∂X.

【 授权许可】

Unknown