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
王丽1
作者信息
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→‖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.
Abstract
The boundary value problem of fractional differential equations with infinite points with parameters and p-La-placian is studied.The existence of unique positive solutions with any given positive parameter λ is obtained.Several definite properties of positive solutions dependent on parameter λ＞0 are given,namely,the positive solution u*λ is continuous,strictly increasing with λ,and lim λ→+∞‖u*λ‖=+∞,limλ→+∞‖u*λ‖=0.The concrete analysis relies on a new theory of operator equations A(x,x)=x and A(x,x)=λx,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-LaplacianKey words
existence and uniqueness/positive solution/fractional differential equation/p-Laplacian引用本文复制引用
基金项目
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)
出版年
2024
NETL
NSTL
万方数据