一类n阶常微分方程边值问题正解的存在性  

Existence of positive solutions of boundary value problems for nth-order ordinary differential equations

作　　者：刘颖 陈逸藻 李琳 LIU Ying;CHEN Yi-zao;LI Lin(College of Science,Shenyang Aerospace University,Shenyang 110136,China;School of mathematics,Liaoning University,Shenyang 110036,China)

机构地区：[1]沈阳航空航天大学理学院,沈阳110136 [2]辽宁大学数学院,沈阳110036

出　　处：《沈阳航空航天大学学报》2018年第1期91-96,共6页Journal of Shenyang Aerospace University

基　　金：国家自然科学基金(项目编号:61403260)

摘　　要：通过一个积分上限函数把一类n阶常微分方程三点边值问题降阶为二阶微分积分方程三点边值问题,又通过格林函数法把微分积分方程边值问题转换为积分算子方程,在方程非线性项满足超线性和次线性的条件下,通过适当选取积分下限,克服了不等式证明中的困难,利用锥上紧算子范数形式的拉伸和压缩不动点定理,证明了这类n阶常微分方程三点边值问题正解的存在性,推广了以前结果,为相关问题的进一步讨论提供了理论基础。The three-point boundary value problem of a class of n-order ordinary differential equations is reduced to a three-point boundary value problem for second-order differential integral equations by an integral upper bound function.The boundary value problem of differential integral equation is transformed into integral operator equation by Green's function method.When the nonlinear term of differential integral equation satisfies superlinear and sublinear condition,the lower limit of integral is properly selected.To overcome the difficulties in the proof of inequalities,the existence of positive solutions for this class of n-order ordinary differential equations with three point boundary value problems is proved by using the extension and contraction fixed point theorems in the norm form of compact operators on cones,which generalizes the previous results.It provides a theoretical basis for further discussion of related problems.

关 键 词：n阶 边值问题 正解 不动点 

分 类 号：O175[理学—数学]