Positive entire solutions for a class of singular nonlinear polyharmonic equations on R2

摘要

In the paper, the existence of positive radially symmetric entire solutions for a class of singular nonlinear polyharmonic equations on R2 is proved. Some properties are obtained. The results of this paper are generalizations of those in Refs. [Math. Z. 67 (1957) 32; Arch. Math. 9 (1958) 308; Proc. R. Soc. Edinburg 82A (1979) 189; Hiroshima Math. J. 17 (1989) 13].