关键词: 双调和方程, 正整解, Lebesgue控制收敛定理, 等度连续, 不动点定理.

Abstract: In this paper, author’s aim is to establish the theorems of existence of positive
radially symmetric entire solutions for a class of singular nonlinear biharmonic equation Δ²u=f(|x|, u,| u|)u^-β (x ∈ Rⁿ, n ≥ 3, β > 0) on Rⁿ with the Schauder-tychonoff fixed point theorem as the principal tool, and presents the properties of the solutions. They enrich and develop the theory and application
of papes [1--5].

Key words: Biharmonic equation, Positive entire solution, Lebesgue dominated covergence theorem, Equicontinuity, Fixed point theorem.