摘要
为了控制电子束的运动轨迹,使其有效地聚焦目标,对电子束聚焦系统数学模型的正椭圆周期解的存在性进行研究.利用Floquet理论得到了该方程的正椭圆周期解存在的条件;然后利用上下解方法和拓扑度的同伦不变性理论,证明了该模型正椭圆周期解的存在性定理,并进行了实例验证.结果表明:对该模型的系数取值范围的界定合理,正椭圆周期解的存在性定理正确,为进一步研究稳定性奠定了基础.
In order to control the moving trace of electron beam and make it focus object effectually, the existence of positive elliptic periodic solution was studied based on the electron beam focusing system model. The condition for the existence of positive elliptic periodic solution was found using Floquet theory; and the theorem of the existence of positive elliptic periodic solution was proved by the method of upper and lower solutions and homotopy invariance theory of topology degree; then an example was given. The results show that the limited ranges of coefficient are reasonable and the theorem is right,which provide a basis for future study of stability.
出处
《中国矿业大学学报》
EI
CAS
CSCD
北大核心
2007年第6期864-868,共5页
Journal of China University of Mining & Technology
基金
国家自然科学基金项目(10771212
10674177)
关键词
电子束聚焦系统模型
椭圆周期解
FLOQUET理论
上下解
拓扑度
electron beam focusing system model
elliptic periodic solution
Floquet theory
upper and lower solution
topology degree
