一类非线性跨共振点边值问题解的存在性

EXISTENCE OF SOLUTIONS FOR A CLASS OF NONLINEAR BOUNDARY PROBLEM ACROSS RESONANCE POINTS

本文讨论了一类高阶线性常微分方程边值问题的非线性扰动问题,在扰动跨共振点时分析了解的存在性.文中使用了分解空间的手段对线性化的单个问题的解的存在唯一性作了细致的分析,并使用Hilbert空间方法将单个线性化的问题解的存在性推广到了非线性问题上,提出了一个简单的存在性充分条件:扰动与共振点存在距离.在文章的最后给出了本文结论的一个简单应用.

In this paper,a class of nonlinear perturbed problem of high ordered linear ordinary differential equations boundary problem is considered and the existence of solutions while the nonlinear perturbation across resonance points is discussed,the space decomposition technique is used to analyze solvability of the linearized equation at the whole space,and Hilbert space method is then used to generalize the local linear results to the original nonlinear problem,a type of simple sufficient conditions, in which o...