Positive Entire Solutions Of Nonlinear Polyharmonic Equations In R\u3csup\u3e2\u3c/sup\u3e

In this paper, the existence of positive, radially symmetric entire solutions for the equations Δmu=f(|x|, u, |∇u|) (m=2,3,...) on R2 is proved. Some properties of the solutions are obtained. The results of this paper are generalizations of these proved in [W. Water, Math. Z 67 (1957) 32-37; W. Water, Arch. Math 9 (1958) 308-312; W. Water, H. Rhee, Proc. Royal Soc. Edinburgh A 82 (1979) 189-192; T. Kusno, C.A. Swanson, Hiroshima Math. J. 17 (1989) 13-28]. © 2002 Elsevier Science Inc. All rights reserved