具p-Laplacian算子分数阶微分方程边值问题的研究

发布时间：2018-06-24 03:15

  本文选题：分数微分方程 + 边值问题　； 参考：《湘潭大学》2017年硕士论文

【摘要】：近些年来,在诸多学科领域,非线性分数阶微分方程有着广泛的应用,而且非线性分数阶微分方程边值问题更是微分方程中的一类重要的问题.随着研究内容的不断深化与研究成果不断呈现,非线性分数阶微分方程占据比重越来越大,其中在微分方程的多个分支中,边值问题的研究尤其重要,其问题的讨论依然在这一方面还需进一步补充与深入.本文第二章主要探讨了如下的具p-Laplacian算子分数阶微分方程两点边值问题正解的存在性与唯一性.其中α ∈ (1,2), β∈(0,1),D0+α是α阶Riemman-iouville分数导数,f是连续函数.Φp是p-Laplacian算子.本文第三章主要探讨了如下的具p-Laplacian算子分数阶微分方程边值问题正解的存在性与唯一性.其中,3α≤4,0β≤1,0μ1.D0+α是α阶Riemman-Liouville分数导数.f是连续函数,Φp是p-Laplacian算子.在第二章、第三章中,我们首先讨论p-Laplacian算子在非负有界区间上的一些性质与集合与集合的关系,然后通过给定非负函数a及非线性函数f的一些适定条件,结合由微分方程转换为积分方程的格林函数,采用非紧测度与不动点定理给出了上述问题的正解存在唯一性准则。
[Abstract]:In recent years, nonlinear fractional differential equations have been widely used in many disciplines, and the boundary value problems of nonlinear fractional differential equations are one of the most important problems in differential equations. With the deepening of the research contents and the continuous presentation of the research results, the proportion of nonlinear fractional differential equations is increasing, among which the study of boundary value problems is particularly important in many branches of differential equations. The discussion of its problem still needs to be further supplemented and deepened in this respect. In chapter 2, we discuss the existence and uniqueness of positive solutions for two-point boundary value problems of fractional differential equations with p-Laplacian operators. Where 伪 鈭，

本文编号：2059753