一类Rn上奇异非线性双调和方程正整解的存在性及性质
The existence and properties of positive entire solutions for a class of singular nonlinear biharmonic equations on Rn
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摘要: 以Schauder-Tychonoff不动点定理为工具,建立了一类Rn上奇异非线性双调和方程Δ2u=f(|x|,u,|▽u|)u-β(n≥3,β0)正的径向对称整体解的存在性定理,并给出了解的有关性质.Abstract: The theorems of existence of positive radially symmetric entire solutions for a class singular nonlinear biharmonic Δ2u=f(|x|,u,|▽u|)u-β(n≥3,β0)on Rn with the Schauder-tychonoff fixed point theorem as the principal are established,and the ralated properties of the solutions were obtained.