非线性项受导数影响的非局部二阶问题正解  

Positive Solutions to Nonlocal Second-Order Problems with Derivative-dependent Nonlinearity

作　　者：宋春蕾 陈伟[1] 张国伟[1] SONG Chunlei;CHEN Wei;ZHANG Guowei(Department of Mathematics,Northeastern University,Shenyang 110819,China)

机构地区：[1]东北大学数学系,辽宁沈阳110819

出　　处：《应用数学》2023年第3期571-577,共7页Mathematica Applicata

基　　金：国家级大学生创新创业训练计划资助项目(S202210145149)。

摘　　要：本文研究一类二阶边值问题,其边值条件具有变号测度的Stieltjes积分,非线性函数包含二阶增长的导数项和无增长约束的函数项.利用Gronwall型不等式对导数项做先验估计,通过不动点指数的方法,获得了正解的存在性结果.In this paper we study a second-order boundary value problem with the boundary value conditions involving Stieltjes integral of sign-changing measure,the nonlinearity contains derivative term of second growth and function term without growth constraint.The priori estimation of the derivative term is done using an inequality of Gronwall type,and the existence of positive solutions is obtained by the method of fixed point index.

关 键 词：正解 不动点指数 锥 Gronwall型不等式 

分 类 号：O175.14[理学—数学]