| 具幂指数型非线性项的发展型p-Kirchhoff方程及其稳态形式 |
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| 引用本文： | 常秀玲,高文杰.具幂指数型非线性项的发展型p-Kirchhoff方程及其稳态形式[J].吉林大学学报(理学版),2002,57(4):729-736. |
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| 作者姓名： | 常秀玲 高文杰 |
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| 作者单位： | 1. 兴安盟广播电视大学, 内蒙古 乌兰浩特 137400; 2. 吉林大学 数学学院, 长春 130012
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| 摘 要： | 考虑一类具幂指数型非线性项的p-Kirchhoff方程初边值问题及其稳态形式. 对于发展型方程, 采用位势井方法, 利用位势井的性质及积分估计, 刻画该问题一般整体解的渐近行为, 并证明位势井深的可达性; 对于稳态问题, 利用Lagrange乘数法给出其基态解的存在性.
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| 关 键 词： | p-Kirchhoff方程 幂指数型非线性项 基态解 渐近行为 |
| 收稿时间： | 2019-01-17 |
An Evolution p-Kirchhoff Equation with Power ExponentialNonlinearity and Its Steady State Form |
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| CHANG Xiuling,GAO Wenjie.An Evolution p-Kirchhoff Equation with Power ExponentialNonlinearity and Its Steady State Form[J].Journal of Jilin University: Sci Ed,2002,57(4):729-736. |
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| Authors: | CHANG Xiuling GAO Wenjie |
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| Institution: | 1. Xing’an League Radio and Television University, Ulanhot 137400, Inner Mongolia Autonomous Region, China;2. College of Mathematics, Jilin University, Changchun 130012, China
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| Abstract: | We considered an initial boundary value problemof a class of p-Kirchhoff equation with exponential nonlinearity and its
steady state form. For the evolution equation, we adopted the potential well method. We characterized the asymptotic behaviors of the general global solutions to the problem and the depth of the potential wellcould be attained by using the properties of potential well and estimates. For the steady state problem, we gave the existence of a ground state
solution by using Lagrange multiplier method. |
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| Keywords: | p-Kirchhoff equation power exponential nonlinearity ground state solution asymptotic behavior
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