带有对数非线性项的p-Kirchhoff型方程的多解性  

Multiplicity of Solutions for p-Kirchhoff Equation with Logarithmic Nonlinearity

作　　者：段碧霄 王淑丽 郭祖记 DUAN Bi-xiao;WANG Shu-li;GUO Zu-ji(College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China)

机构地区：[1]太原理工大学数学学院

出　　处：《中北大学学报（自然科学版）》2019年第5期385-389,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学青年基金资助项目(11601363);山西省自然科学基金资助项目(201601D102001)

摘　　要：研究了一类带有对数非线性项的p-Kirchhoff型方程的多解性问题.利用山路定理,Ekeland变分原理和对数Sobolev不等式,在有界区上讨论了方程非平凡解的多重性,证明了泛函满足山路定理的条件,结合Ekeland变分原理,得到结论方程至少含有两个非平凡解.Multiple solutions for p -Kirchhoff equation with logarithmic nonlinearity were investigated. Multiplicity of nontrivial solutions were discussed on a bounded domain by Mountain Pass Theorem, Ekeland's variational principle and logarithmic Sobolev inequality. It proved that the functional satisfied conditions of Mountain Pass Theorem and combined with Ekeland's variational principle, it drew a conclusion that the problem had at least two nontrivial solutions.

关 键 词：山路定理 EKELAND变分原理 对数SOBOLEV不等式 非平凡解 

分 类 号：O177.91[理学—数学]