摘要
为了研究一类带有组合非线性项的基尔霍夫方程的径向解的存在性,首先对方程中的V、K、f函数做出合理的假设,然后主要运用变分原理,先得到此方程相对应的能量泛函,之后证明了方程相对应的泛函满足PS条件且存在有界且收敛的PS子序列,最后利用山路引理得到该问题的径向解的存在性。
In order to study a type of Kirchhoff problem when the sublinear term is involved in nonlinearity, we firstly give some suitable assumptions about V,K,f functions. According to the variational method, its solutions can be regarded as critical points of the energy function. Supposing all the assumptions hold, then the energy function satisfies the PS condition and there exists a convergent PS subsequence which is bounded. Finally we use the mountain pass theorem to obtain the existence of one non-trivial solution.
作者
刘紫玉
韩伟
LIU Ziyu;HAN Wei(School of Science, North University of China, Taiyuan 030051, China)
出处
《重庆理工大学学报(自然科学)》
CAS
北大核心
2019年第4期203-208,共6页
Journal of Chongqing University of Technology:Natural Science
基金
山西省青年科学基金项目(2015021001)
中北大学杰出青年基金项目(JQ201604)
山西省高等学校科技创新项目(201802085)
关键词
基尔霍夫方程
变分方法
山路引理
径向解
PS条件
Kirchhoff problem
variational method
mountain pass theorem
radial solutions
PS condition