关于奇异的非线性双调和方程正整解

Positive Entire Solutions to Singular Nonlinear Biharmonic Equations

本文研究了一类Rn(n≥3)上带奇异性的非线性双调和方程Δ2u=f(|x|,u,|▽u|) u-β,(β>0,x∈Rn,n≥3),给出了该类方程有正的整体解的充分必要条件,以及解的性质.

Abstract： In this paper, the writer studies a class of singular nonlinear biharmonic equation Δ2u=f（｜x｜,u,｜▽u｜） u-β,（β〉0,x∈Rn,n≥3）,and some conditions are presented, under which the equations have positive entire solutions for the class, together with the properties of the solutions.