A LIOUVILLE-TYPE THEOREM FOR HIGHER ORDER ELLIPTIC SYSTEMS OF HE NON-LANE-EMDEN TYPE

作者：Arthur Frank^*; Yan Xiaodong^*

来源：Communications on Pure and Applied Analysis, 2016, 15(3): 807-830.

DOI：10.3934/cpaa.2016.15.807

• Liouville theorem
• Henon Lane Emden
• positive solutions

We prove there are no positive solutions with slow decay rates to higher order elliptic system
{(-Delta)(m)(u)=vertical bar x vertical bar(a)v(p) (-Delta)(m)(v)=vertical bar x vertical bar(b)u(q) in R-N
if p >= 1, q >= 1 (p,q) not equal (1,1) satisties 1+a/N/p+1 + 1+b/N/q+1 > 1 - 2m/N and
max(2m(p+1)+a+bp/pq-1, 2m(q+1)+aq+b/pq-1) > N - 2m - 1.
Moreover, if N - 2m+1 or N - 2m+2, this system admits no positive solutions with slow decay rates if p >= 1, q >= 1, (p,q) not equal (1, 1) satisfies 1/p+1, 1/q+1, > 1 - 2m/N.

• 出版日期2016-5