Abstract

We consider the uniqueness of solutions of the equation Δ²u = e^u in four-dimensional Euclidean space. Our main result is that the solutions are all classical ones, provided that the energy of the solutions is finite and the diffusion of the solutions decays to zero at infinity. The method we used in this paper is known as the method of moving spheres.

Keywords

conformally invariant equation, symmetry, moving sphere method

Mathematical Subject Classification

Primary: 35J60, 58G35

Secondary: 53C21

Authors