Non-radial solutions to a bi-harmonic equation with negative exponent

Abstract

We prove the existence of non-radial entire solution to $${\Delta }^{2}u+u^{-q}=0\text{in }{\mathbb{R}}^3,u>0,$$ for $q>1$. This answers an open question raised by P. J. McKenna and W. Reichel (E. J. D. E. \textbf{37} (2003) 1-13).

References in corpus (1)

• Classification of solutions to the higher order Liouville's equation on R^{2m}