含梯度项非线性椭圆方程古典解的存在性
Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms.
作者信息
Li Yongxiang, Ma Weifeng
机构信息
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China.
出版信息
Entropy (Basel). 2022 Dec 15;24(12):1829. doi: 10.3390/e24121829.
This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term -Δu=f(x,u,∇u) on Ω restricted by the boundary condition u|∂Ω=0, where Ω is a bounded domain in RN with sufficiently smooth boundary ∂Ω, N≥2, and f:Ω¯×R×RN→R is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity f(x,ξ,η) when |(ξ,η)| is small or large enough.
本文研究在边界条件(u|\partial\Omega = 0)限制下，(\Omega)上具有非线性梯度项(-\Delta u = f(x, u, \nabla u))的椭圆方程解的存在性，其中(\Omega)是(R^N)中边界(\partial\Omega)足够光滑的有界区域，(N\geq2)，且(f:\overline{\Omega}\times R\times R^N\rightarrow R)连续。当(|(\xi, \eta)|)足够小或足够大时，在关于非线性项(f(x, \xi, \eta))的一些不等式条件下，得到了经典解和正解的存在性结果。
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