The existence of positive entire solutions to singular nonlinear polyharmonic equations in Rn

摘要

In this paper, the existence of positive radially symmetric entire solutions for the equation Δmu=f(|x|,|∇u|)u−β (m⩾2) on Rn (n⩾3) is proved. Some properties of the solutions are obtained. The results of this paper may be regarded of results in [Math. Z. 67 (1957) 32; Arch. Math. 9 (1958) 308; Proc. Royal Soc. Edinburgh 82A (1979) 189; Hiroshima Math. J. (1989) 13].