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带梯度项的半线性椭圆方程整体解的存在性
引用本文:薛洪涛.带梯度项的半线性椭圆方程整体解的存在性[J].数学研究及应用,2015,35(4):417-424.
作者姓名:薛洪涛
作者单位:烟台南山学院数学物理教学部, 山东 烟台 265713
基金项目:山东省高等学校科技计划项目(Grant No.J12LI54).
摘    要:By a sub-supersolution method and a perturbed argument,we show the existence of entire solutions for the semilinear elliptic problem-△u + a(x)|▽u|~q = λb(x)g(u),u 0,x ∈ R~N,lim(|x|→∞) u(x) = 0,where q ∈(1,2],λ 0,a and b are locally Holder continuous,a ≥0,b 0,(?)x∈ R~N,arid g ∈ C~1((0,∞),(0,∞)) which may be both possibly singular at zero and strongly unbounded at infinity.

关 键 词:半线性椭圆方程    整体解    梯度项    存在性
收稿时间:2014/7/18 0:00:00
修稿时间:2015/4/25 0:00:00

Existence of Entire Solutions for Semilinear Elliptic Problems with Convection Terms
Hongtao XUE.Existence of Entire Solutions for Semilinear Elliptic Problems with Convection Terms[J].Journal of Mathematical Research with Applications,2015,35(4):417-424.
Authors:Hongtao XUE
Institution:Mathematics and Physics Teaching Department, Yantai Nanshan University, Shandong 265713, P. R. China
Abstract:By a sub-supersolution method and a perturbed argument, we show the existence of entire solutions for the semilinear elliptic problem $- \Delta u +a(x)|\nabla u|^q=\lambda b(x)g(u)$, $u>0$, $x\in \mathbb R^N$, $\lim_{|x|\rightarrow \infty} u(x)=0$, where $q\in (1,2]$, $\lambda>0$, $a$ and $b$ are locally H\"{o}lder continuous, $a\geq 0$, $b>0$, $\forall x\in \mathbb R^N$, and $g\in C^1((0,\infty), (0,\infty))$ which may be both possibly singular at zero and strongly unbounded at infinity.
Keywords:semilinear elliptic equation  entire solution  convection term  existence
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