[1]吴燕林,钱晓涛.一类次临界增长非局部问题的无穷多解[J].延边大学学报(自然科学版),2019,45(04):299-302.
　WU Yanlin,QIAN Xiaotao.Infinitely many solutions for a class of nonlocalproblem with subcritical growth[J].Journal of Yanbian University,2019,45(04):299-302.
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一类次临界增长非局部问题的无穷多解

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第45卷 期数: 2019年04期 页码: 299-302 栏目: 应用科学研究 出版日期: 2020-01-15
Title:
Infinitely many solutions for a class of nonlocal problem with subcritical growth
文章编号:
1004-4353(2019)04-0299-04
作者:
吴燕林;  钱晓涛
( 阳光学院 基础教研部, 福建 福州 350015 )
Author(s):
WU Yanlin;  QIAN Xiaotao
( Department of Basic Teaching and Research, Yango University, Fuzhou 350015, China )
关键词:
非局部问题;  非平凡解;  无穷多解;  变分方法
Keywords:
nonlocal problem;  nontrivial solution;  infinitely many solutions;  variational method
分类号:
O175.2
文献标志码:
A
摘要:
在有界域上研究一类次临界增长的非局部问题.应用对称山路定理,在更一般的条件下证明了所考虑的问题有无穷多个解.该结果拓展了文献[1]的研究结果.
Abstract:
We study a class of nonlocal problem with subcritical growth in a bounded domain. Under the more general condition, we prove the existence of infinitely many solutions for the considered problem by using the symmetric mountain pass theorem. Our result can be viewed as an extension of literature [1] concerning the existence of solutions.

参考文献/References:

[1] YIN G, LIU J. Existence and multiplicity of nontrivial solutions for a nonlocal problem[J]. Boundary Value Problems, 2015,2015(26):1-7.
[2] LEI C Y, LIAO J F, SUO H M. Multiple positive solutions for nonlocal problems involving a sign-changing potential[J]. Electronic Journal of Differential Equations, 2017,2017(9):1-8.
[3] LEI C Y, CHU C M, SUO H M. Positive solutions for a nonlocal problem with singularity[J]. Electronic Journal of Differential Equations, 2017,2017(85):1-9.
[4] ZHANG J, ZHANG Z Y. Existence of nontrivial solution for a nonlocal problem with subcritical nonlinearity[J]. Advances in Difference Equations, 2018,2018(359):1-8.
[5] WANG Y, SUO H M, LEI C Y. Multiple positive solutions for a nonlocal problem involving critical exponent[J]. Electronic Journal of Differential Equations, 2017,2017(275):1-11.
[6] 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(4):302-305.
[7] WILLEM M. Minimax Theorems[M]. Birkhäuser Boston, 1996:133-134.
[8] FURTADO M, SILVA J, XAVIER M. Multiplicity of self-similar solutions for a critical equation[J]. Journal of Differential Equations, 2013,254(7):2732-2743.
[9] 陆文端.微分方程中的变分方法[M].北京:科学出版社,2003:8-9.

相似文献/References:

[1]刘春晗,王建国.四阶椭圆方程非平凡解的多重性[J].延边大学学报(自然科学版),2015,41(02):111.
　LIU Chunhan,WANG Jianguo.Multiplicity of nontrivial solutions for fourth-order elliptic equations[J].Journal of Yanbian University,2015,41(04):111.
[2]刘春晗.一类 p -拉普拉斯椭圆方程的多重解[J].延边大学学报(自然科学版),2018,44(03):194.
　LIU Chunhan.Multiple solutions for a class of p-Laplacian elliptic equations[J].Journal of Yanbian University,2018,44(04):194.

备注/Memo

收稿日期: 2019-10-25 基金项目: 福建省中青年教师教育厅科技类项目(JAT170772)
作者简介: 吴燕林(1984—),女,副教授,研究方向为非线性分析及其应用.

更新日期/Last Update: 2020-01-15