A MONOTONICITY FORMULA AND LIOUVILLE-TYPE THEOREMS FOR STABLE SOLUTIONS OF THE WEIGHTED ELLIPTIC SYSTEM

作者：Hu, Liang-Gen^*

来源：Advances in Differential Equations, 2017, 22(1-2): 49-76.

• MORSE INDEX SOLUTIONS
• PARTIAL REGULARITY
• R-N
• BIHARMONIC PROBLEMS
• BOUNDED DOMAINS
• SMALL DIFFUSION
• WEAK SOLUTIONS
• EQUATIONS
• CLASSIFICATION

In this paper, we are concerned with the weighted elliptic system
{-Delta u = vertical bar x vertical bar(beta)upsilon(upsilon) -Delta u = vertical bar x vertical bar(alpha) vertical bar u vertical bar(p-1)u, in R-N
where N >= 5, alpha > -4, 0 <= beta < N - 4, p > 1 and upsilon = 1. We first apply Pohozaev identity to construct a monotonicity formula and reveal their certain equivalence relation. By the use of Pohozaev identity, mono tonicity formula of solutions together with a blowing down sequence, we prove Liouville-type theorems for stable solutions (whether positive or sign-changing) of the weighted elliptic system in the higher dimension.

• 出版日期2017-2
• 单位宁波大学