Stieltjes积分边值条件下四阶问题的多重正解  

Multiple Positive Solutions of Fourth-Order Problems Subject to Stieltjes Integral Boundary Conditions

作　　者：宋春蕾 陈伟[1] 张国伟[1] SONG Chun-lei;CHEN Wei;ZHANG Guo-wei(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：《数学的实践与认识》2022年第11期216-224,共9页Mathematics in Practice and Theory

基　　金：国家级大学生创新创业训练计划资助项目(202110145083)。

摘　　要：应用五泛函不动点定理,当非线性函数在几个闭区域上满足一些不等式约束条件时,证明了具有Stieltjes积分边值条件的四阶问题存在多重正解,其非线性项含有未知函数的导数.通过一个多点型和积分型混合边值条件的例子,说明结论的可应用性,例子中的多点边值条件含有变号的系数,积分边值条件中积分核是变号的超越函数.Using five functional fixed point theorem,the existence of multiple positive solutions is proved for fourth-order problems with Stieltjes integral boundary value conditions when the nonlinearity is restrained by some inequalities on several closed domains,which includes the derivatives of unknown functions.The applicability of result is illustrated by means of an example subject to mixed boundary conditions involving multi-point with coefficients of both signs and integral with sign-changing transcendental function kernel.

关 键 词：正解 锥 五泛函不动点定理 

分 类 号：O175.8[理学—数学]