含p-Laplacian和参数的分数阶微分方程无穷点边值问题正解的唯一性  

Uniqueness of Positive Solutions for Infinite Point Boundary Value Problems of Fractional Differential Equations with p-Laplacian and Parameters

作　　者：王丽[1] Wang Li(Jinzhong University,Jinzhong 030619,China)

机构地区：[1]晋中学院,山西晋中030619

出　　处：《廊坊师范学院学报（自然科学版）》2024年第3期14-20,29,共8页Journal of Langfang Normal University(Natural Science Edition)

基　　金：山西省自然科学基金青年项目(202303021212267);晋中学院2023年教学改革创新项目(Jg202362)。

摘　　要：研究含参数和p-Laplacian的无穷点分数阶微分方程的边值问题。任意给定一个正参数λ时,方程存在唯一的正解,给出依赖于参数λ>0的正解的几个明确性质,即正解u_(λ)^(*)连续,关于λ严格递增,且limλ→+∞||u_(λ)^(*)||=+∞,limλ→0^(+)||u_(λ)^(*)||=0。具体分析依赖于算子方程A(x,x)=x和A(x,x)=λx的新理论,其中A是一个混合单调算子。最后给出一个具体例子作为所获结论的应用。The boundary value problem of fractional differential equations with infinite points with parameters and p-Laplacian is studied.The existence of unique positive solutions with any given positive parameter A is obtained.Several definite propertiesof positivesolutions dependent on parameterλ>Oare given,namely,the positive solution u_(λ)^(*)is continuous,stricty increasing with,and limλ→+∞||u_(λ)^(*)||=+∞,limλ→0^(+)||u_(λ)^(*)||=0.The concrete analysis relies on a new theory of operator equations A(x,x)=x and A(x,x)=Ax,and A is a mixed monotone operator.Finally,a concrete example is given as an application of the conclusions.

关 键 词：存在唯一性 正解 分数阶微分方程 P-LAPLACIAN 

分 类 号：O175.8[理学—数学]