含导函数Stieltjes积分边界条件下二阶问题的正解  

Positive Solutions for Second Order Problems under Stieltjes Integral Boundary Conditions with Derivative

作　　者：计倩 张国伟[1] JI Qian;ZHANG Guowei(Department of Mathematics,College of Science,Northeastern University,Shenyang 110819,China)

机构地区：[1]东北大学理学院数学系,沈阳110819

出　　处：《应用泛函分析学报》2020年第4期193-206,共14页Acta Analysis Functionalis Applicata

摘　　要：本文研究了一类含导函数Stieltjes积分边值条件下二阶边值问题的正解.由于边值条件中带有导数,导致讨论过程与已有文献不同,并且给出相应的格林函数.应用不动点指数理论证明非线性项f(x,y,z)关于x,y有超(次)线性增长情形下方程正解的存在性.通过两个具体例子进行说明理论结果的有效性,例子中边值条件包含积分型与多点型的形式.In this paper,we study positive solutions for a class of second order problems under Stieltjes integral boundary conditions with derivative.Due to the derivative in the boundary conditions,the procedure of discussing is different from one in previous literature,and Green’s function corresponding to the problem is given.The fixed point index theory is applied to prove the existence of positive solutions when the nonlinear term f(x,y,z) has superlinear or sublinear growth on x and y.The validity of the theoretical results is illustrated by two concrete examples,in which the boundary conditions include the forms of integral and multi-point types.

关 键 词：正解 不动点指数 锥 

分 类 号：O175.14[理学—数学] O177.91[理学—基础数学]