Positive Liouville theorems and asymptotic behavior for p-Laplacian type elliptic equations with a Fuchsian potential
arXiv:1003.5452
Abstract
We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form Q'(u):= - pLaplace(u) + V |u|^{p-2} u = 0 in X, where X is a domain in R^d, d > 1, and 1<p<infty. We assume that the potential V has a Fuchsian type singularity at a point zeta, where either zeta=infty and X is a truncated C^2-cone, or zeta=0 and zeta is either an isolated point of a boundary of X or belongs to a C^2-portion of the boundary of X.
39 pages. Stronger results in the radial case, other results and conclusions are unchanged, considerable restructuring of the paper, introduction is modified, typos corrected, references added