【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.更多还原

【Abstract】 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.更多还原