带Riemann-Stieltjes积分条件的三阶边值问题的单调正解

Multiple Monotone Positive Solutions to 3rd-Order Boundary Value Problems Involving Riemann-Stieltjes Integral Conditions

研究了一类带Riemann-Stieltjes积分条件的非线性三阶非局部边值问题,将边值问题正解存在性的研究转化为扰动Hammerstein积分方程的研究,通过构造Green(格林)函数及讨论其性质,运用推广的Leggett-Williams型不动点定理,得到了至少存在3个和2n-1个正解的存在性准则,所得结果推广和改进了最近文献中的结果,并充分反映了非线性项含导数对正解存在性研究的影响.主要结果由实例加以阐述.

A class of 3rd-order nonlocal boundary value problems（ BVPs） with R iemann-Stieltjes integral conditions were studied. The existence of positive solutions to BVPs was explored via perturbed Hammerstein integral equations. Through the construction of the Green functions and discussion on their properties,the existence criterion for at least 3 or 2n- 1 positive solutions was obtained by means of the generalization of the Leggett-Williams fixed point theorem. The results generalize and improve some known results of the latest literatures,and fully reflect the influence of nonlinear terms involving derivatives on the existence of positive solutions. An example was also included to illustrate the main results.