[1]钱晓涛,石志高.一类Kirchhoff型方程解的存在性和多重性[J].延边大学学报(自然科学版),2018,44(04):302-305.
　QIAN Xiaotao,SHI Zhigao.Existence and multiplicity of solutions for a class of Kirchhoff type equation[J].Journal of Yanbian University,2018,44(04):302-305.
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一类Kirchhoff型方程解的存在性和多重性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第44卷 期数: 2018年04期 页码: 302-305 栏目: 基础科学研究 出版日期: 2018-12-30
Title:
Existence and multiplicity of solutions for a class of Kirchhoff type equation
作者:
钱晓涛1;  石志高2
( 1.福建农林大学 金山学院, 福建 福州 350002; 2.福建江夏学院, 福建 福州 350108 )
Author(s):
QIAN Xiaotao1;  SHI Zhigao2
( 1.Jinshan College of Fujian Agriculture and Forest University, Fuzhou 350002, China; 2.Fujian Jiangxia College, Fuzhou 350108, China )
关键词:
Kirchhoff型方程;  下方无界;  存在性;  多重性;  变分方法
Keywords:
Kirchhoff type equation;  unbounded from below;  existence;  multiplicity;  variational method
分类号:
O175.2
文献标志码:
A
摘要:
研究一类全空间上的下方无界Kirchhoff型方程,通过引进满足某种假设的位势函数使得所考虑问题的紧性得到恢复.首先证明带该位势函数的非线性项所对应的泛函是弱连续和连续可导的,然后证明所考虑问题的泛函在某个水平下是紧的,最后通过验证满足山路定理的几何条件证明该问题至少有一个非负非平凡解.由于所考虑问题具有对称性,因此同时又证得该问题至少存在一个非正非平凡解.
Abstract:
On the whole space, we study a class of Kirchhoff type equation which is unbounded from below. To recover the compactness for the considered problem, we introduce a potential function satisfied some assumption. Firstly, the weak continuity and the continuous derivation of the functional corresponding to the nonlinear term are showed. Subsequently, the functional of the problem is proved to satisfy compact condition under some level. Lastly, the existence of non-negative nontrivial solution is established by Mountain Pass Theorem. Meanwhile, the symmetry of the problem implies that there exists another non-positive nontrivial solution.

参考文献/References:


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备注/Memo

收稿日期: 2018-11-04 基金项目: 福建省中青年教师教育科研项目(JAT170893,JT180586)
作者简介: 钱晓涛(1984—),男,博士,讲师,研究方向为非线性分析及其应用.

更新日期/Last Update: 2018-12-30