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非线性多调和方程
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  nonlinear poly-harmonic equations
     On Positive Entire Solutions to Singular Nonlinear Poly-Harmonic Equations in R~2
     关于奇异非线性多调和方程的正整体解
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     Existence of Entire Solutions to Nonlinear Poly-harmonic Equations in R~2
     关于非线性多调和方程的整体解的存在性
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     ON POSITIVE ENTIRE SOLUTIONS TO SINGULAR, NONLINEAR POLY-HARMONIC EQUATIONS IN R~N(N ≥ 3)
     R~N上奇异非线性多调和方程的正整体解
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     In this paper two-dimensional nonlinear poly-harmonic equations of the form are considered, where p>1, b0, n is an integer (n1), xa*:=|x|a-1x, xR, a>0, and f:+RRR R+ is a continuous function.
     本文主要研究形如:△ ((△nu)p ) + f(|x|, u, ?u)=0, x∈R2的非线性多调和方程的整体解, ?
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  “非线性多调和方程”译为未确定词的双语例句
     Positive Entire Solutions to the Singular Nonlinear Polyharmonic Equations
     奇非线性多调和方程的整体正解(英文)
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  相似匹配句对
     Multiple-soliton solutions of the nonlinear partial differential equation
     非线性偏微分方程孤子解
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     NONLINEAR INCENTIVE STRATEGIES WITH MULTIPLE NONCOOPERATIVE FOLLOWERS
     随从非线性诱导策略
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     (3)the non-linear Multi-user detector.
     (3)非线性用户检测器。
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     Solving Nonlinear Multivariable Equation Systems by Neural Networks
     用神经网络解非线性方程
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     On Application of Solving Nonlinear Multivariable Equation Systems by Neural Networks
     人工神经网络在非线性方程组中的应用
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In this paper N dimensional singular, nonlinear poly harmonic equations of the following form Δ nu=f(|x|,u,|u|)u -β ,x∈ R Nare considered, where n is an integer (n≥2), and f∶\[0,∞)×(0,∞)×\[0,∞)→\[0,∞) is continuous function. It is obtained that some sufficient and necessary conditions for the existence of infinitely many positive symmetric entire solutions which are asymptotic to positive constant multiples of |x| 2n-2  as |x|→∞. [WTHZ]

本文研究形如Δnu=f( |x| ,u ,| u|)u-β ,x∈RN 的奇异非线性多调和方程在RN(N ≥ 3)上的正整体解 ,给出了该方程具有无穷多个其渐进阶刚好为 |x|2n-2 的正整体解的充分与必要条件

In this paper, two dimensional singular nonlinear poly harmonic equation of the form Δ((Δ\+nu)\+\{p-1*\}) = f(|x|, u, |u|)u\+\{-β\},\ x∈R\+2 is considered, where p>1, β≥0, n is an integer (n≥1),ξ\+\{α*\}:=|ξ|\+\{α-1\}ξ,ξ∈R,α>0. and f: \-+×R\-+×\-+→R\-+ is a continuous function. It is shown that any positive radially symmetric entire solution grows at least as fast as positive constant multiples of |x|\+\{2n\}(\%log\%|x|)\+\{1/(p-1)\} as |x|→∞ . It is given that some sufficient conditions and...

In this paper, two dimensional singular nonlinear poly harmonic equation of the form Δ((Δ\+nu)\+\{p-1*\}) = f(|x|, u, |u|)u\+\{-β\},\ x∈R\+2 is considered, where p>1, β≥0, n is an integer (n≥1),ξ\+\{α*\}:=|ξ|\+\{α-1\}ξ,ξ∈R,α>0. and f: \-+×R\-+×\-+→R\-+ is a continuous function. It is shown that any positive radially symmetric entire solution grows at least as fast as positive constant multiples of |x|\+\{2n\}(\%log\%|x|)\+\{1/(p-1)\} as |x|→∞ . It is given that some sufficient conditions and necessary conditions for the existence of infinitely many positive symmetric entire solutions which are asymptotic to positive constant multiples of |x|\+\{2n\}( log |x|)\+\{1/(p-1)\} as |x|→∞ . The results can be extended to certain equations of more general form, e.g., Δ((Δ\+nu)\+\{p-1*\})=f(|x|, u, |u|,|u\+2u|,\:,|u|\+\{2n-1\})u\+\{-β\},\ x∈R\+2.

该文主要研究形如Δ( (Δnu) p- 1*) =f( | x| ,u,| u| ) u-β,  x∈ R2的奇异非线性多调和方程在 R2 上的正整体解 ,此处 p>1 ,β≥ 0是常数 ,n是自然数 ,f:R+ × R+×R+ →R+ 是一个连续函数 ,ξα*:=| ξ|α- 1ξ,ξ∈R,α>0 .证明了这种解 u必无界且其渐进阶 (当n→∞时 u作为无穷大量的阶 )不低于 | x| 2 nlog| x| ,给出了该方程具有无穷多个其渐进阶刚好为 | x| 2 nlog| x|的正整体解的充分与充分必要条件 .这些结论可以推广到更一般的方程中去

The existence and multiplicity results on the positive entire solutions of a class of singular nonlinear polyharmonic equations in R n are established. The main tool in the proof is the Schauder-Tychonov fixed point theorem. Two examples are given to illustrate the application of the main theorems.

证明了具有奇性的一类非线性多调和方程在Rn(n≥ 3)上的整体正解的存在性和多解性 ,用两个具体的例子说明定理的应用 .

 
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