一类具低阶项的非线性椭圆方程解的研究  

Study on the Solutions of a Class of Nonlinear Degenerate Elliptic Equations with Lower Order Terms

作　　者：黄琴 邹维林 HUANG Qin;ZOU Wei-lin(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2024年第2期56-60,88,共6页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(11461048,11801259);江西省自然科学基金(20202BABL201009)。

摘　　要：本文主要研究一类具低阶项的非线性椭圆方程解的性质。通过选取适当的检验函数,利用先验估计方法和经典的逼近理论证明了问题弱解的存在性与正则性,揭示了零阶项系数与自由项相互作用的正则化效应。In this paper,we mainly study a class of nonlinear elliptic equations with lower-order terms.By selecting appropriate test functions,using a prior estimation method and classical approximation theory,we prove the existence and regularity of weak solutions to such problems,revealing the regularization effect of the interaction between the zero-order coefficient and the free term.

关 键 词：非线性椭圆方程 存在性 正则化效应 

分 类 号：O175.26[理学—数学]