LIU Chunhan.Existence of nontrivial solutions for a class of biharmonic equations[J].Journal of Yanbian University,2016,42(03):203-206.
一类双调和方程的非平凡解的存在性
- Title:
- Existence of nontrivial solutions for a class of biharmonic equations
- 分类号:
- O175.25
- 文献标志码:
- A
- 摘要:
- 利用山路引理,讨论了非线性项在负无穷远处是渐近线性而在正无穷远处是超线性的一类双调和方程,且获得了该方程的非平凡解.所得结论推广了文献[3]和文献[5]的相应定理.
- Abstract:
- By using the Mountain pass Lemma, when the nonlinear term is asymptotically linear at the negative infinity but superlinear at the positive infinity, a class of biharmonic equations at resonance are discussed. The existence of nontrivial solutions is proved. The resevant theorems of the literature [3] and [5] are generalized.
参考文献/References:
[1] 伍芸,姚仰新,柯敏.含Hardy位势的双调和方程特征值问题[J].山东大学学报(理学版),2008,49(9):81-84.
[2] Adimurthi Grossi M, Santra S.Optimal Hardy-Rellich inequalities, maximun principle and related eigenvalue problem[J]. J Funct Anal, 2006,240(1):36-83.
[3] 刘春晗,王建国.一类渐近线性椭圆方程非平凡解的存在性[J].郑州大学学报(理学版),2014,46(1):5-9.
[4] 裴瑞昌.非线性椭圆型方程的存在性问题与定性分析[D].西安:西北大学,2011.
[5] 伍芸,何少通,沈尧天.一类渐近线性双调和方程非平凡解的存在性[J].数学学报,2011,54(1):9-14.
[6] Zhang Zhitao. Varitional, topological, and partial order methods with their applications[M]. Springer, 2013.
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(03):111.
备注/Memo
收稿日期: 2016-07-02 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(J12LI53); 齐鲁师范学院青年教师科研基金资助项目(2014L1001)