劈形算符
欧米茄
椭圆曲线
数学
订单(交换)
非线性系统
组合数学
功能(生物学)
类型(生物学)
纯数学
数学分析
物理
量子力学
生物
进化生物学
经济
生态学
财务
作者
Youssef Akdim,Abdelmoujib Benkirane,Mostafa El Moumni
摘要
We give an existence result for strongly nonlinear elliptic equations of the form \[ -{\rm div}(a(x,u,\nabla u))+g(x,u,\nabla u)+H(x,\nabla u) = \mu\ \text{in}\ \Omega, \] where the right hand side belongs to $L^1(\Omega)+W^{-1,p'}(\Omega)$ and $- {\rm div}(a(x,u,\nabla u))$ is a Leray--Lions type operator with growth $|\nabla u|^{p-1}$ in $\nabla u$. The critical growth condition on $g$ is with respect to $\nabla u$ and no growth condition with respect to $u$, while the function $H(x,\nabla u)$ grows as $|\nabla u|^{p-1}$.
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