一类非线性四阶椭圆型方程的弱解存在性问题  

Existence of Weak Solutions for a Class ofNonlinear Fourth Order Elliptic Equations

作　　者：王博 李秀梅[1] WANG Bo;LI Xiu-mei(School of Science,Dalian Jiaotong University,Dalian 116028,Liaoning,China)

机构地区：[1]大连交通大学理学院,辽宁大连116028

出　　处：《兰州文理学院学报（自然科学版）》2022年第5期13-15,共3页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：针对一类四阶椭圆型方程的弱解问题,首先在分部积分的意义下,给出其弱解的定义;其次构造极小元泛函,将问题转化为相应泛函的极值元并证明极值元的存在性,找到弱解;最后给出弱解的唯一性.In this paper,the definition of weak solutions for a class of fourth-order elliptic equations was first given in the sense of integration by parts,then the functional extremum element was constructed,the problem was transformed into the extremum element of the corresponding functional and the existence of extremum element was proved,the weak solution was found,and finally the uniqueness of weak solution was proved.

关 键 词：椭圆型方程 弱解 极小元泛函 存在性 

分 类 号：O175.29[理学—数学]