[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):111-115.
　LIU Chunhan,WANG Jianguo.Multiplicity of nontrivial solutions for fourth-order elliptic equations[J].Journal of Yanbian University,2015,41(02):111-115.
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四阶椭圆方程非平凡解的多重性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第41卷 期数: 2015年02期 页码: 111-115 栏目: 基础科学研究 出版日期: 2015-05-30
Title:
Multiplicity of nontrivial solutions for fourth-order elliptic equations
作者:
刘春晗; 王建国
齐鲁师范学院 数学学院, 山东 济南 250013
Author(s):
LIU Chunhan;  WANG Jianguo
School of Mathematics, Qilu Normal University, Jinan 250013, China
关键词:
山路引理;  临界群;  非平凡解
Keywords:
Mountain Pass Lemma;  critical group;  nontrivial solution
分类号:
O175.25
文献标志码:
A
摘要:
在非共振的情况下讨论了一类不满足Ambrosetti-Rabinowitz型增长条件的四阶椭圆方程.首先,证明泛函Φ满足(PS)条件.其次,证明泛函Φ满足山路引理的其他条件.最后,利用Morse理论和山路引理获得了方程的3个非平凡解.
Abstract:
The fourth-order elliptic equations at no resonance are discussed without assuming Ambrosetti-Rabinowitz type growth conditions. Firstly, we prove that the functional Φ satisfies(PS)condition. Secondly, we prove that the functional Φ satisfies the other conditions of Mountain Pass Lemma. Finally, three nontrivial solutions are obtained by using Morse Theory and Mountain Pass Lemma.

参考文献/References:

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相似文献/References:

[1]刘春晗.一类双调和方程的非平凡解的存在性[J].延边大学学报(自然科学版),2016,42(03):203.
　LIU Chunhan.Existence of nontrivial solutions for a class of biharmonic equations[J].Journal of Yanbian University,2016,42(02):203.

备注/Memo

收稿日期: 2014-05-12 作者简介: 刘春晗(1981—),男,副教授,研究方向为非线性泛函分析及其应用.基金项目: 国家自然科学基金资助项目(10971179); 山东省高等学校科技计划项目(J12L153); 齐鲁师范学院青年教师科研基金资助项目(2014L1001)

更新日期/Last Update: 2015-05-30