奇异非线性$p-$调和方程的一类正整体解

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.

POSITIVE ENTIRE SOLUTIONS TO SINGULAR, NONLINEAR $p$-HARMONIC EQUATIONS

Suppose $p>1, \beta\geq0$ are constants, $n$ is a positive integer and $f:\overline{R}_+\times R_+\times\overline{R}_+ \rightarrow R $ is a continuous function. This paper investigates $N$-dimensional singular, nonlinear $p$-harmonic equations of the form $$ \Delta(| \Delta^nu | ^{p-2} (\Delta ^nu)) = f (| x |, u, | \nabla u |) u^{-\beta},\q x\in R^N (N\geq3), $$ 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 $| x |\rightarrow\infty$.