本文關鍵詞：時標上幾類積分邊值問題多解性研究　出處：《云南大學》2015年碩士論文　論文類型：學位論文

  更多相關文章： 時標 p-Laplacian算子 不動點定理 積分邊值條件 多解性 錐

【摘要】：本論文就時標上的積分邊值問題多解性作出一些研究,并得到了一系列新的結(jié)果. 本論文的組織結(jié)構(gòu)安排如下, 第一章,主要介紹本文的研究背景及研究價值.第二章主要介紹相關概念、定義及定理. 第三章,研究如下時標上三階帶p-Laplacian算子動力方程積分邊值問題的多個正解的存在性：其中.令ρ:=ad+ac+bc區(qū)間[0,1]T：-[0,1]∩T,并且0,1∈T,本文用φp(u)表示p-Laplacian算子,即Φp(u)=|u|p-2u,p1,(Φp)-1=Φq,1/p+1/q=1通過利用Legggt-Williams不動點定理的推廣定理獲得了時標上三階帶p-Laplacian算子的動力方程積分邊值問題至少存在三個正解的判定定理； 第四章,考慮以下時標上帶積分邊值問題三階非線性微分方程的多解性：其中,區(qū)間[0,1]T：=[0.1]∩T,并且0,1∈T,φ：R→R連續(xù)同胚正同態(tài),并且滿足O(0)=0.并根據(jù)Leggtt-Williams不動點定理的推廣定理,得到了時標上三階動力方程積分邊值問題至少存在三個正解的充分條件.
[Abstract]:In this paper, we make some research on the multi solution of the integral boundary value problem on the time scale, and get a series of new results.
The organizational structure of this paper is arranged as follows.
The first chapter mainly introduces the research background and value of the study. The second chapter mainly introduces the related concepts, definitions and theorems.
The third chapter, the following research on time scales of three order p-Laplacian operator with dynamic equations with integral boundary value problems of the existence of multiple positive solutions: one. Make p: =ad+ac+bc T and 0,1 [0,1]T:-[0,1] interval, and T, with the P diameter (U) said that with the p-Laplacian operator, P (U) =|u|p-2u, P1 (P) -1=, Phi Q, 1/p+1/q=1 by using the theorem of Legggt-Williams theorem is obtained when the underlying problem has at least three positive solutions theorems of integral dynamic equation with p-Laplacian operator on the three order boundary value;
The fourth chapter, consider the following multiple solutions with integral boundary value problem of three order nonlinear differential equations on scales: the range of [0,1]T:=[0.1] T, and 0,1, T, R, R: Phi continuous homeomorphism is homomorphism, and meet the O (0) =0. and according to the extension of Leggtt-Williams fixed point theorem theorem, obtain the sufficient conditions for the existence of three positive solutions of the boundary integral three order dynamic equation on time scales.

【學位授予單位】：云南大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O175.8

【參考文獻】

相關期刊論文 前1條

1 劉萍;索劍鋒;杜瑞霞;;時間尺度上的一階三點邊值問題的多個正解分析(英文)[J];安徽大學學報(自然科學版);2011年06期

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本文編號：1383565