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非线性p-调和方程
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  nonlinear p-harmonic equations
    POSITIVE ENTIRE SOLUTIONS TO SINGULAR, NONLINEAR p-HARMONIC EQUATIONS
    奇异非线性p-调和方程的一类正整体解
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    In this paper N-dimensional singular, nonlinear p-harmonic equations of the following form ((膗)p-1*) = f(|x|, u, |u|)u-b, xRN are considered, where p>1, b0, xa*:=|x|a-1x,xR,a>0, and f: +R+R+RR is a continuous function.
    本文研究形如: ((膗)p-1*) = f(|x|, u, |u|)u-b 的奇异非线性p-调和方程在RN上的正整体解,此处1<pN/2,?
短句来源
    This paper investigates N-dimensional singular, nonlinear p-harmonic equations of the form and gives some sufficient conditions under which the equations have infinitely many radial positive entire solutions which are asymptotic to positive constant multiples of |x|(2n-2) as |x|→∞.
    本文研究形如的奇异非线性p-调和方程的正整体解,给出了该类方程具有无穷多个其渐近阶刚好为|x|(2n-2)(当|x|→∞时)的径向对称的正整体解的若干充分条件.
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In this paper N-dimensional singular, nonlinear p-harmonic equations of the following form ((膗)p-1*) = f(|x|, u, |u|)u-b, xRN are considered, where p>1, b0, xa*:=|x|a-1x,xR,a>0, and f: +R+R+RR is a continuous function. It is given that some sufficient conditions for the existence of infinitely many positive symmetric entire solutions which are bounded or asymptotic to positive constant multiples of |x|(2p-N)/(p-1) when N<2p, and log t when N=2p as |x|.

本文研究形如: ((膗)p-1*) = f(|x|, u, |u|)u-b 的奇异非线性p-调和方程在RN上的正整体解,此处10 , 给出了该类方程具有无穷多个(1)有界的,(2)其渐进阶刚好为 |x| (2p- N)/(p-1)(当p>N/2)或log t(当p=N/2)的正整体解的条件.

Abstract Suppose p>1, β≥0 are constants, n is a positive integer and f:R+×R+×R+→R is a continuous function. This paper investigates N-dimensional singular, nonlinear p-harmonic equations of the form and gives some sufficient conditions under which the equations have infinitely many radial positive entire solutions which are asymptotic to positive constant multiples of |x|(2n-2) as |x|→∞.

设p>1,β≥0是常数, n是自然数, 是一个连续函数.本文研究形如的奇异非线性p-调和方程的正整体解,给出了该类方程具有无穷多个其渐近阶刚好为|x|(2n-2)(当|x|→∞时)的径向对称的正整体解的若干充分条件.

 
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