本文選題：delta-nabla分數(shù)階階差分方程 + 邊值問題�。� 參考：《延邊大學(xué)》2017年碩士論文

【摘要】：近年來,隨著數(shù)學(xué)學(xué)科的不斷發(fā)展,越來越多的分數(shù)階差分方程數(shù)學(xué)模型被人們發(fā)現(xiàn),使得人們對于分數(shù)階差分方程的近似計算要求越來越高.而隨著分數(shù)階差分方程的發(fā)展,人們對分數(shù)階差分方程的研究不再僅限于純理論的研究,還應(yīng)用到生物學(xué)、物理學(xué)等實際問題中,因此分數(shù)階差分方程逐漸成為學(xué)者們關(guān)注的熱門領(lǐng)域之一.對分數(shù)階差分方程進一步的研究可幫助我們完善微、差分方程理論與應(yīng)用的基礎(chǔ)性工作,并為我們研究其他函數(shù)方程提供了大量支撐.本文主要研究的是如下帶p-拉普拉斯算子的delta-nabla分數(shù)階差分邊值問題通過變換的技巧,將上述原帶p-拉普拉斯算子的delta-nabla分數(shù)階差分邊值問題轉(zhuǎn)化為如下分數(shù)階差分邊值問題并對轉(zhuǎn)化后的分數(shù)階差分方程利用上下解方法和Schauder不動點定理證明其正解的存在性,從而得到原方程正解的存在性結(jié)論.同時,我們也利用單調(diào)迭代技術(shù)研究變換后的分數(shù)階差分邊值問題,得到了其正解的近似解,從而推斷出原邊值問題近似解的求法.
[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.
【學(xué)位授予單位】：延邊大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.8

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本文編號：1849770