本文選題：適型分?jǐn)?shù)階導(dǎo)數(shù) + 邊值問題�。� 參考：《山東科技大學(xué)》2017年碩士論文

【摘要】：本文用錐上的不動點(diǎn)理論考慮具有適型分?jǐn)?shù)階導(dǎo)數(shù)的幾類分?jǐn)?shù)階邊值問題的正解的存在性和多解性,并給出相應(yīng)問題的Laplace變換.根據(jù)內(nèi)容,全文共六章:第一章,介紹微分方程邊值問題的研究背景與發(fā)展概況.第二章,介紹分?jǐn)?shù)階微分方程的相關(guān)概念與性質(zhì);給出具有適型分?jǐn)?shù)階微分方程邊值問題的Green函數(shù)以及具有適型分?jǐn)?shù)階導(dǎo)數(shù)的線性齊次問題Laplace變換;最后給出本文所需要的一些工具.第三章,研究具有適型分?jǐn)?shù)階導(dǎo)數(shù)的非線性邊值問題的正解.首先給出此問題的積分算子并證明其全連續(xù)性;然后給出研究結(jié)果,即對非線性項進(jìn)行控制,再利用錐壓縮拉伸不動點(diǎn)定理證明研究問題的正解的存在性和多解性;最后給出所研究問題的Laplace變換.兩個例子說明主要結(jié)果.第四章,在上一章的基礎(chǔ)上,研究具有適型分?jǐn)?shù)階導(dǎo)數(shù)的非線性特征值問題.解的存在性結(jié)果是通過給出特征值準(zhǔn)則而得到的,證明過程也利用不動點(diǎn)定理.第五章,研究具有適型分?jǐn)?shù)階導(dǎo)數(shù)的P-Laplacian邊值問題的正解.給出邊值問題所對應(yīng)的積分算子,利用Laplace算子的性質(zhì)證得積分算子的全連續(xù)性,進(jìn)而利用不動點(diǎn)定理證明研究問題的正解的存在性和多解性.第六章,本文的總結(jié)和展望.
[Abstract]:In this paper, we use the fixed point theory on cone to consider the existence and multiple solvability of the positive solutions of several class of fractional boundary value problems with a suitable fractional derivative, and give the Laplace transformation of the corresponding problems. In the first chapter, the research background and development of the boundary value problems of differential equations are introduced. The second chapter introduces fractional differential. The related concepts and properties of the equation; give the Green function of the boundary value problem with an adaptive fractional differential equation and the linear homogeneous problem Laplace transformation with a suitable fractional derivative. Finally, some tools needed in this paper are given. The third chapter, the positive solution of the nonlinear boundary value problem with an appropriate fractional order number is studied. The integral operator of the problem is proved to be full continuity, and then the research results are given, that is, to control the nonlinear term, and then to prove the existence and multi solution of the positive solution of the research problem by using the fixed point theorem of the cone compression drawing. Finally, the Laplace transformation of the problem is given. Two examples are given to explain the main results. The fourth chapter is the basis of the previous chapter. The nonlinear eigenvalue problem with a suitable fractional derivative is studied. The existence result of the solution is obtained by giving the eigenvalue criterion. It is proved that the process also uses the fixed point theorem. In the fifth chapter, the positive solution of the P-Laplacian boundary value problem with a suitable fractional derivative is studied. The integral operator corresponding to the boundary value problem is given, and Lapla is used. The nature of the CE operator proves the full continuity of the integral operator, and then uses the fixed point theorem to prove the existence and multi solvability of the positive solution of the research problem. The sixth chapter, the summary and the prospect of this paper.

【學(xué)位授予單位】：山東科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.8

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

1 董曉玉;白占兵;張偉;;具有適型分?jǐn)?shù)階導(dǎo)數(shù)的非線性特征值問題的正解[J];山東科技大學(xué)學(xué)報(自然科學(xué)版);2016年03期

2 武華華;孫蘇菁;;基于變分方法的四階邊值問題的多重正解[J];山東科技大學(xué)學(xué)報(自然科學(xué)版);2014年02期

3 倪小虹,葛渭高;一類半無窮區(qū)間問題非負(fù)解的存在性[J];北京理工大學(xué)學(xué)報;2003年06期

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本文編號：1797370