带P-拉普拉斯算子的delta-nabla分数阶差分边值问题正解的存在性

发布时间：2018-05-05 23:44

本文选题：delta-nabla分数阶阶差分方程 + 边值问题　；参考：《延边大学》2017年硕士论文

【摘要】：近年来,随着数学学科的不断发展,越来越多的分数阶差分方程数学模型被人们发现,使得人们对于分数阶差分方程的近似计算要求越来越高.而随着分数阶差分方程的发展,人们对分数阶差分方程的研究不再仅限于纯理论的研究,还应用到生物学、物理学等实际问题中,因此分数阶差分方程逐渐成为学者们关注的热门领域之一.对分数阶差分方程进一步的研究可帮助我们完善微、差分方程理论与应用的基础性工作,并为我们研究其他函数方程提供了大量支撑.本文主要研究的是如下带p-拉普拉斯算子的delta-nabla分数阶差分边值问题通过变换的技巧,将上述原带p-拉普拉斯算子的delta-nabla分数阶差分边值问题转化为如下分数阶差分边值问题并对转化后的分数阶差分方程利用上下解方法和Schauder不动点定理证明其正解的存在性,从而得到原方程正解的存在性结论.同时,我们也利用单调迭代技术研究变换后的分数阶差分边值问题,得到了其正解的近似解,从而推断出原边值问题近似解的求法.
[Abstract]:In recent years, with the development of mathematics, more and more mathematical models of fractional difference equations have been discovered, which makes the approximate calculation of fractional difference equations more and more demanding. With the development of fractional difference equation, the study of fractional difference equation is no longer limited to pure theory, but also applied to biology, physics and other practical problems. Therefore, fractional difference equation has gradually become one of the hot fields that scholars pay attention to. The further study of fractional difference equations can help us to perfect the basic work of the theory and application of differential equations and provide us with a lot of support for the study of other functional equations. In this paper, the following delta-nabla fractional difference boundary value problems with pLaplacian operator are studied. In this paper, the delta-nabla fractional difference boundary value problem with pLaplacian operator is transformed into the following fractional difference boundary value problem. The existence of positive solutions for the transformed fractional difference equation is proved by using the upper and lower solution method and Schauder fixed point theorem. The existence of positive solution of the original equation is obtained. At the same time, we also use monotone iterative technique to study the fractional difference boundary value problem after transformation, and obtain the approximate solution of its positive solution, thus infer the approximate solution of the original boundary value problem.
【学位授予单位】：延边大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.8

【参考文献】