Rn上带奇异性的非线性双调和方程的正整解

Abstract

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 withthe 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.

CLC Number:

35J30

Xu Xingye. The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rⁿ[J].Acta mathematica scientia,Series A, 2009, 29(1): 87-93.

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The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rⁿ

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The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rn

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The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rⁿ