一类多点共振方程组边值问题正解的存在性

Existence of positive solutions for multi-point resonance systems of differential equations with boundary value conditions

求解共振微分方程边值问题解的存在性比较困难,要得到共振微分方程边值问题的正解更加困难。针对研究领域中这一问题,着重研究了一类多点共振微分方程组边值问题正解的存在性。在前人研究成果的基础上,选取的不同的算子,将方程扩展为方程组。通过在合适的空间中定义恰当的范数使之成为Bananch空间,利用O'Regan和Zima所研究出来的范数形式的Leggett-Williams定理,对非线性项做出合理的假设条件,得到了共振微分方程组边值问题正解的存在性定理。

It is difficult to study the existence of solutions for boundary value problems of differential equations at resonance,moreover,to get positive solutions of boundary value problems for differential equations at resonance is more difficult.To research this problem,the existence of positive solutions for a couple of different equations with multi-point boundary value conditions at resonance is studied.On the basis of previous researches,choosing a different operator,the equation is extended to a couple of different equations.By defining the correct norm in the product spaces which become Banach spaces,and using the Leggett-Williams norm-type theorem due to O'Regan and Zima,the nonlinear term satisfies reasonable assumptions,and the existence of positive solutions for a coupled of different equations with multi-point boundary value conditions at resonance is obtained.