一类非线性微分方程组的无穷可解性  

Infinitely Many Solutions of a System of Nonlinear Differential Equations

作　　者：徐自立[1] 刘进生[2] 

机构地区：[1]中州大学信息工程学院,河南郑州450044 [2]太原理工大学理学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2011年第1期47-50,共4页Journal of North University of China(Natural Science Edition)

摘　　要：研究一类具有变分结构的非线性微分方程组两点边值问题的无穷可解性.在非线性项为奇函数及相关的基本假设条件下,利用非线性泛函分析中的变分方法,结合拓扑度理论、临界点理论,特别是Morse理论与临界群的概念与性质,证明了该问题存在无穷多个解.此方程组是现有文献中许多模型的推广与一般化,因而所得结论更具有普遍性.The infinite solvability of the two-point boundary value problem of a class of nonlinear differential equations with variational structure was investigated.Under the assumptions that the involved nonlinear terms are odd functions and other basic conditions,the existence of infinitely many solutions was proved by using the variational method in nonlinear functional analysis,together with the topological degree theory and critical point theory,especially the Morse theory and the concept and properties of critical groups.The model generalizes many corresponding models in recent literatures and the conclusion is more universal.

关 键 词：方程组 无穷多解 临界点 临界群 

分 类 号：O175[理学—数学]