Positive entire solutions of nonlinear polyharmonic equations in R2

摘要

In this paper, the existence of positive, radially symmetric entire solutions for the equations on 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].