| 具有渐进非线性项的Kirchhoff型方程的正解（英文） |
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| 引用本文： | 许丽萍,陈海波.具有渐进非线性项的Kirchhoff型方程的正解（英文）[J].应用数学,2019,32(4):900-909. |
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| 作者姓名： | 许丽萍 陈海波 |
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| 作者单位： | 1. 河南科技大学数学与统计学院, 河南 洛阳 471000; 2. 中南大学数学与统计学院, 湖南 长沙 410075 |
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| 基金项目： | Supported by the National Natural Science Foundation of China(11671403,11671236);by Major State Basic Research of Higher Education of He,nan Provincial of China(17A110019) |
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| 摘 要： | 本文研究一类非线性Kirchhoff型方程.非线性项函数f(x,u)在无穷远处关于u是渐进线性或渐进非线性的.若位势函数V(x)和非线性项f(x,u)满足给定的条件,本文在工作空间缺乏紧性嵌入的情形下获得该方程正解的存在性.
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| 关 键 词： | Kirchhoff型方程 渐进非线性 变分法 正解 |
Positive Solutions for Kirchhoff-Type Equations with an Asymptotically Nonlinearity |
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| XU Liping,CHEN Haibo.Positive Solutions for Kirchhoff-Type Equations with an Asymptotically Nonlinearity[J].Mathematica Applicata,2019,32(4):900-909. |
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| Authors: | XU Liping CHEN Haibo |
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| Institution: | (Department of Mathematics and Statistics, Henan University of Scienceand Technology, Luoyang 471000, China;School of Mathematics and Statistics,Central South University, Changsha 410075, China) |
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| Abstract: | We focus on a class of nonlinear Kirchhoff-type equation. The nonlinear function f(x;u) is either asymptotically linear or asymptotically nonlinear with respect to u at infinity. Under certain conditions on the potential function V (x) and the nonlinear term f(x;u), the existence of positive solutions is obtained without using the compactness of embedding of the working space. |
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| Keywords: | Kirchhoff-type equation Asymptotically nonlinear Variational method Positive solution |
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