| 一类带变位势的临界指数增长的椭圆型方程组正解 |
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| 引用本文： | 万优艳.一类带变位势的临界指数增长的椭圆型方程组正解[J].南通工学院学报(自然科学版),2013(3):82-85. |
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| 作者姓名： | 万优艳 |
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| 作者单位： | 江汉大学数学与计算机科学学院,湖北武汉430056 |
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| 基金项目： | 湖北省教育厅科学技术研究计划指导性项目（B2013155,Q20083401） |
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| 摘 要： | 研究了一类带变位势的临界指数增长的椭圆型方程组．通过使用变分法得到的研究结果表明：虽然方程组带变位势，但方程组的能量泛函在零点附近存在局部极小值点，且该极小值点为方程组的正解．此外，当方程组的扰动项趋于零时．该正解也趋于零．
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| 关 键 词： | 临界指数 变位势 椭圆型方程组 正解 |
Discussion on Positive Solutions of an Elliptic System with Variable Potentials Involving Critical Sobolev Exponents |
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| Authors: | WAN You-yan |
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| Institution: | WAN You-yan (School of Mathematics and Computer Science, Jianghan University, Wuhan 430056, China) |
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| Abstract: | An elliptic system with variable potentials involving critical Sobolev exponents is studied. By the variation methods, results show that： although the system with variable potentials, there exists a local minimum point of the en- ergy functional related to the system which is near zero, and the local minimum point is a positive solution of this sys- tem. Moreover, this positive solution tends to be zero when the perturbed term goes to zero. |
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| Keywords: | critical exponents variable potentials elliptic system positive solutions existence |
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