一类n阶完全边值问题正解的存在性

Existence of Positive Solution to a Class of n-order Complete Boundary Value Problems

运用锥上的不动点理论和特殊的导数估计方法,讨论了一类n阶非线性微分方程两点完全边值问题正解的存在性。利用格林函数给出了对应的线性情形下解的存在唯一性结论,针对线性情形的唯一解,讨论了解的导数估计结果,在非线性项f满足次线性增长的前提下,得到了n阶非线性微分方程两点完全边值问题正解的存在性。结合所得定理,给出了应用实例。

By using the fixed point theory on cone and special derivative estimation method,the existence of positive solution to two-point complete boundary value problems in a class of-order nonlinear differential equationsis discussed.As to the unique solution to linear case,the conclusion of the existence and uniqueness of the corresponding solution in linear case is obtained by using Green′s function and the result of derivative estimation of the solution is discussed.Under the condition that the nonlinear term f satisfying sublinear growth,the existence of positive solution to nonlinear two-point complete boundary value problems is obtained.Combined with the obtained theorem,an application example is given.