一类具低阶项的非线性退化椭圆方程解的存在性  

Existence of Solutions to a Class of Nonlinear Degenerate Elliptic Equation with Lower Order Terms

作　　者：李鑫鑫[1] 邹维林 LI Xin-xin;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）》2019年第4期26-30,共5页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(11461048,11801259);江西省教育厅科技项目(GJJ170604)。

摘　　要：研究了一类具低阶项的非线性退化椭圆方程,其中低阶项相对于梯度u的增长条件为次p次增长,而且随着解u变大,此类方程的微分主算子可能是非强制的。为克服上述困难,利用先验估计方法和逼近理论,证明了问题解的存在性与正则性。In this paper, we mainly study a class of degenerate elliptic equations with lower order terms which growth like sub-porder growth with respect to the modulus of the gradient of u. Furthermore, the main differential operator may not be coercive on the same space as u becomes large. In order to overcome this difficulty stated above, by using a prior estimation method and approximation theory, we proved the existence and regularity of solutions to such problems.

关 键 词：退化椭圆方程 次p次增长 非正则数据 

分 类 号：U458[建筑科学—桥梁与隧道工程]