| 具有非线性奇异项的半线性椭圆方程解的存在性 |
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| 引用本文： | 初颖,孙艳,高文杰.具有非线性奇异项的半线性椭圆方程解的存在性[J].吉林大学学报(理学版),2015,53(6):1211-1213. |
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| 作者姓名： | 初颖 孙艳 高文杰 |
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| 作者单位： | 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 |
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| 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m1,1α2-1/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.
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| 关 键 词： | 非线性 奇异项 半线性椭圆方程 存在性 |
| 收稿时间： | 2015-05-14 |
Existence of Solutions to a Class of Semilinear Elliptic Equations with Nonlinear Singular Terms |
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| CHU Ying,SUN Yan,GAO Wenjie.Existence of Solutions to a Class of Semilinear Elliptic Equations with Nonlinear Singular Terms[J].Journal of Jilin University: Sci Ed,2015,53(6):1211-1213. |
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| Authors: | CHU Ying SUN Yan GAO Wenjie |
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| Institution: | 1. School of Science, Changchun University of Science and Technology, Changchun 130022, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | 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, provingthe 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. |
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| Keywords: | nonlinear singular term semilinear elliptic equation existence |
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