具有非线性奇异项的半线性椭圆方程解的存在性  

Existence of Solutions to a Class of Semilinear Elliptic Equations with Nonlinear Singular Terms

作　　者：初颖[1] 孙艳[1] 高文杰[2] 

机构地区：[1]长春理工大学理学院,长春130022 [2]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2015年第6期1211-1213,共3页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11271154)

摘　　要：采用逼近的方法,借助逼近问题当n=1时解可积的充分条件和先验估计技巧,研究具有非线性奇异项的半线性椭圆方程解的存在性,证明了当m>1,1<α<2-1/m时该问题弱解的存在性,从而得到了方程右端权函数f(x)的可积性以及非线性奇异项对解决该问题的影响.We investigated the existence of the solutions to a class of semilinear elliptic equations with nonlinear singular terms using the technique of approximation with the help of the integrability of the solution to the first step of the approximate problem and some priori estimates,proving the existence of weak solutions for this problem when m〉 1,1〈α〈2-1/m so as to get the effect of the summability of the weighted function f（x）and the nonlinear singular term on the right hand side of the equation.

关 键 词：非线性 奇异项 半线性椭圆方程 存在性 

分 类 号：O175.8[理学—数学]