A Liouville-type theorem for higher order elliptic systems

作者：Yan Xiaodong^*

来源：Journal of Mathematical Analysis and Applications, 2012, 387(1): 153-165.

DOI：10.1016/j.jmaa.2011.08.081

• Liouville theorem
• Higher order elliptic system

We prove there are no positive radial solutions for higher order elliptic system %26lt;br%26gt;{ (-Delta)(m)u = v(p) %26lt;br%26gt;in R(N) %26lt;br%26gt;(-Delta)(m)v = u(q) %26lt;br%26gt;if 1/p+1 + 1/q+1 %26gt; 1 - 2m/N. We also show there are no positive solutions to the system under the additional assumption that max (2(p+1)/pq - 1, 2(q+1)/pq - 1) %26gt;= N - 2m/m. The proof in the radial case uses Rellich%26apos;s identity and the proof in the general case relies on growth estimates of the spherical average of the solution.

• 出版日期2012-3-1