具有对流项的(2,p)-Laplace方程非负解的存在性  

Existence of non-negative solution for(2,p)-Laplace equation with convection term

作　　者：张沐 黄永艳[1] ZHANG Mu;HUANG Yongyan(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《纺织高校基础科学学报》2022年第2期79-82,共4页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(12071266);山西省基础研究计划项目(201801D211001)。

摘　　要：在非线性项f满足适当的限制性条件下,研究具有对流项的(2,p)-Laplace方程非负解的存在性。根据非线性项f的限制性条件,得到了Nemytskii算子的连续性和有界性;利用(2,p)-Laplace算子的性质以及Sobolev紧嵌入定理,将方程转化为一个不动点问题;利用锥理论和不动点指数理论解决不动点问题,得到了方程非负解的存在性。Under appropriate restrictive conditions on the nonlinear term f,the existence of non-negative solution for(2,p)-Laplace equation with convection term were considered.According to the restrictive conditions on the nonlinear term f,the continuity and boundedness of Nemytskii operator are obtained;Using the properties of(2,p)-Laplace operator and Sobolev compact embedding theorem,the equation is transformed into a fixed point problem.Using the cone theory and fixed point index theory to solve the fixed point problem,the existence of non-negative solution of the equation is obtained.

关 键 词：(2 p)-Laplace方程 解的存在性 锥理论 不动点指数理论 

分 类 号：O177.91[理学—数学] O175.2[理学—基础数学]