摘要
文章研究的是在R 4中的基尔霍夫型问题,-(a+b∫R^4|▽u|2dx)△u+V(x)u=K(x)u^3+μf(u),(*)其中a,b都是大于零的常数,V,f,K具有合适的条件.通过利用推广的山路定理,得到了方程(*)解的存在性和非存在性.通过利用Nehari流形,我们可以得到方程(*)具有正的基态解.
We study the following Kirchhoff type problem-(a+b∫R^4|▽u|2dx)△u+V(x)u=K(x)u^3+μf(u)in R^4,(*)where a,b>0 are constants,suitable conditions are imposed on V,f,K.By using the generalized Mountain-pass Theorem,the existence and non-existence results is solutions of(*).By using the Nehari manifold,a ground state solution for equation(*)is abtained.
作者
赵亚茹
孙燕
栾世霞
ZHAO Yaru;SUN Yan;LUAN Shixia(School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong,PRC)
出处
《曲阜师范大学学报（自然科学版）》
CAS
2020年第1期19-28,共10页
Journal of Qufu Normal University(Natural Science)
基金
National Natural Science Foundation of China(11471187,11571197)
