非线性二阶常微分方程的两点边值问题  

Two-Point Boundary Value Problem for Nonlinear Second Order Differential Equation

作　　者：胡志刚[1] 陈太勇[1] 李波[2] 章美月[1] 

机构地区：[1]中国矿业大学应用数学系,江苏徐州221008 [2]徐州师范大学数学系,江苏徐州221116

出　　处：《上海第二工业大学学报》2005年第2期49-53,共5页Journal of Shanghai Polytechnic University

基　　金：中国矿业大学科研预研基金资助项目(No.OK4066);中国矿业大学青年科学基金(No.OK4481)

摘　　要：非线性常微分方程边值问题是微分方程研究领域中一个较为实际,其发展也较为活跃的一个分支.非线性二阶常微分方程两点边值问题解的存在性的研究方法有很多,如迭代法、上下解方法、度理论、临界点理论等.现利用拓扑横截定理,考虑了二阶常微分方程两点边值问题在组合边界条件下的解的存在性,对二阶常微分方程两点边值问题所对应的辅助问题作先验界估计,并利用拓扑横截定理,得到了边值问题解的存在性,推广了一些已有结果.Two-point boundary value problem subject to nonlinear second order differential equation is applied in engineer and technology science. The existence of solutions for two-point boundary value problem subject to nonlinear second order differential equation is studied by many methods, such as iterative method, lower and upper solutions method, degree theory , Critical theory and etc. The existence of solutions for two-point boundary value problem subject to nonlinear second order differential equation with mixed boundary conditions is studied by using topological transversality theorem, and some known results are improved.

关 键 词：边值问题 拓扑横截定理 微分方程 

分 类 号：O175.8[理学—数学]