摘要
研究一类全空间上的下方无界Kirchhoff型方程,通过引进满足某种假设的位势函数使得所考虑问题的紧性得到恢复.首先证明带该位势函数的非线性项所对应的泛函是弱连续和连续可导的,然后证明所考虑问题的泛函在某个水平下是紧的,最后通过验证满足山路定理的几何条件证明该问题至少有一个非负非平凡解.由于所考虑问题具有对称性,因此同时又证得该问题至少存在一个非正非平凡解.
On the whole space,we study a class of Kirchhoff type equation which is unbounded from below.To recover the compactness for the considered problem,we introduce a potential function satisfied some assumption.Firstly,the weak continuity and the continuous derivation of the functional corresponding to the nonlinear term are showed.Subsequently,the functional of the problem is proved to satisfy compact condition under some level.Lastly,the existence of non-negative nontrivial solution is established by Mountain Pass Theorem.Meanwhile,the symmetry of the problem implies that there exists another non-positive nontrivial solution.
作者
钱晓涛
石志高
QIAN Xiaotao;SHI Zhigao(Jinshan College of Fujian Agriculture and Forest University,Fuzhou350002,China;Fujian Jiangxia College,Fuzhou 350108,China)
出处
《延边大学学报（自然科学版）》
CAS
2018年第4期302-305,共4页
Journal of Yanbian University（Natural Science Edition）
基金
福建省中青年教师教育科研项目(JAT170893
JT180586)
