一类二阶非线性无穷多点边值问题的正解

Existence of Positive Solutions for a Second Order Nonlinear ∞-point Boundary Value Problems

利用非线性泛函分析中Banach空间的锥理论和不动点定理,通过构造合适的锥,在非线性函数满足超线性或次线性的条件下,讨论了一类二阶非线性微分方程无穷多点边值问题,得到了其正解的存在性结果,推广了已有文献中的一些结论.

In this paper,by constructing a special cone and using the fixed point theorem as well as cone theory in Banach spaces,we obtain the existence of positive solutions to a nonlinear second-order ordinary differential equations of ∞-point boundary value problem,when the nonlinear term satisfies superlinear growth condition or sublinear growth condition.The results improved those in known literatures.