Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms

被引：1

作者：

Li, Yongxiang ^{[1
]}

Ma, Weifeng ^{[1
]}

机构：

[1] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

来源：

ENTROPY | 2022年 / 24卷 / 12期

关键词：

elliptic equation; gradient term; classical solution; positive solution; QUASI-LINEAR EQUATIONS; POSITIVE SOLUTIONS; RADIAL SOLUTIONS; DEPENDENCE; THEOREMS; FORM;

D O I：

10.3390/e24121829

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term -Delta u = f (x, u, del u) on Omega restricted by the boundary condition u vertical bar(partial derivative Omega) = 0, where Omega is a bounded domain in R-N with sufficiently smooth boundary partial derivative Omega, N >= 2, and f : (Omega) over bar x R x R-N -> R. is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity f (x, xi, eta) when vertical bar(xi, eta)vertical bar is small or large enough.

引用

页数：9

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