摘要
本文首先介绍了Kirchhoff方程物理背景及其应用,并且介绍了用变分方法研究Kirchhoff方程得到的已有成果,指出渐近3-线性的非线性项的Kirchhoff方程还没有人研究.最后利用临界点理论中的山路引理证明了具有在原点和无穷原点都渐近3-线性的一般非线性项的Kirchhoff方程解的存在性结果.
In this paper, we firstly introduced the physical background, application and the research achievements by using variational methods of Kirchhoff equations, and pointed that there is no results for Kirchboff equations with asymptotically 3-linear nonlinearity. Finally, the existence of solutions is ob- tained for Kirchhoff equations with the general nonlinearity which is asymptotically 3-linear at zero and at infinity by using the Mountain Pass Lemma in critical point theory.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2014年第3期447-450,共4页
Journal of Sichuan University(Natural Science Edition)
基金
湖北省教育厅科学技术研究计划重点项目(D20122501)
