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R2 are considered, where 
doi:10.1016/S0096-3003(00)00169-7 
Copyright © 2002 Elsevier Science Inc. All rights reserved.
Positive entire solutions of nonlinear polyharmonic equations in
Available online 7 January 2002.
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Abstract
In this paper, the existence of positive, radially symmetric entire solutions for the equations Δmu=f(|x|,u,|
u|) (m=2,3,…) 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].
Author Keywords: Polyharmonic equation; Positive entire solution; Lebesgue dominated convergence theorem; Relatively compact and equicontinuity
