| 一类具有非局部项和临界项椭圆方程的正解 |
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| 引用本文： | 柳鸠,廖家锋,唐春雷.一类具有非局部项和临界项椭圆方程的正解[J].数学学报,2018,61(3):411-430. |
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| 作者姓名： | 柳鸠 廖家锋 唐春雷 |
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| 作者单位： | 1.西南大学数学与统计学院 重庆 400715;2.黔南民族师范学院数学与统计学院 都匀 558000;3.西华师范大学数学与信息学院 南充 637002 |
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| 基金项目： | 国家自然科学基金（11471267）；贵州省教育厅自然科学研究项目（黔教合KY字[2015]453）；黔南民族师范学院非线性分析科研创新团队（Qnsyk201606） |
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| 摘 要： | 本文研究下列具有临界项的Kirchhoff型方程(a+b∫_R~3|▽u|~2+V/(x)u~2]dx).-△u+V(x)u]=μf(x,u)+K(x)u~5,x∈R~3,其中a,b,μ0,位势函数V,K满足一些恰当的条件,非线性项f满足超三次或超线性增长性条件.利用山路定理,得到三个存在性结果.
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Positive Solution for a Class of Elliptic Equations Involving Nonlocal Term and Critical Term |
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| Jiu LIU,Jia Feng LIAO,Chun Lei TANG.Positive Solution for a Class of Elliptic Equations Involving Nonlocal Term and Critical Term[J].Acta Mathematica Sinica,2018,61(3):411-430. |
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| Authors: | Jiu LIU Jia Feng LIAO Chun Lei TANG |
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| Institution: | 1.School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China;2.School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun 558000, P. R. China;3.School of Mathematics and Information, China West Normal University, Nanchong 637002, P. R. China |
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| Abstract: | In the paper, the following Kirchhoff-type equations with critical exponent (a+b∫R3|?u|2+V(x)u2]dx)·-△u+V(x)u]=μf(x,u)+K(x)u5,x∈R3, is studied, in which a, b, μ > 0, the potential functions V, K satisfy some conditions and the nonlinear term f verifies sup-cubic or sup-linear growth. With the aid of the mountain pass theorem, three existence results are obtained. |
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| Keywords: | Kirchhoff-type equations Mountain pass theorem critical exponent |
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