带p—Laplacian算子分数阶微分方程多点边值问题解存在性是关于对写作微分方程论文范文与课题研究的大学硕士、相关本科毕业论文微分方程解法论文开题报告范文和相关文献综述及职称论文参考文献资料下载有帮助。
摘 要 利用不动点定理,研究带有p-Laplacian算子的分数阶微分方程多点边值问题解的存在性,得到边值问题至少存在一个解的充分条件.
关键词 分数阶微分方程;p-Laplacian算子;存在性;不动点定理
中图分类号 O175.8 文献标识码 A 文章编号 10002537(2016)01008005
Exitence of Solutions for Fractions Multipoint
Boundary Value Problem with p-Laplacian Operator
LV Qiuyan1, LIU Wenbin2*, TANG Min2, SHEN Tengfei2, CHENG Lingling2
(1.Dongshan High School, Suzhou 215107, China;
2.College of Science, China University of Mining and Technology, Xuzhou 221116, China)
Abstract
This paper presents a study on the existence of solutions for the fractional multi-point boundary value problem with p-Laplacian operator. Making use of the fixed-point theorem, we obtained sufficient conditions to guarantee the existence of at least one solution for the boundary value problem.
Key words fractional differential equation; p-Laplacian operator; existence; fixed point theorem
显然,问题(4)满足定理2.1的假设条件.因此,至少存在一个解.
参考文献:
[1] LAKSHMIKANTHM V. Theory of fraction functional differential equations[J]. Nonlinear Anal: TMA, 2008,69(10):3333733343.
[2] ABDELKADER B. Secondorder boundary value problems with integral boundary conditions[J]. Nonlinear Anal, 2009,70(1):364371.
[3] DELBOSCO D. Fractional calculus and function spaces[J]. J Fract Calc,1994,6:4553.
[4] LI C, LUO X, ZHOU Y. Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations[J]. Comput Math Appl, 2010,59(3):13631375.
[5] LEIBENSON L S. General problem of the movement of a compressible fluid in a porous medium[J]. Izvestiia Akademii Nauk Kirgizskoi SSR, 1945,9:710.
[6] SHEN T, LIU W, CHEN T, et al. Solvability of fractional m-point boundary value problems with p-Laplacian operator at resonance[J]. Electr J Diff Equ, 2014(58):110.
[7] JIANG W. Solvability of boundary value problem with p-Laplacian at resonance[J]. Bound Value Probl, 2014(1):36.
[8] 申腾飞,刘文斌,宋文耀.一类带有p-Laplacian算子分数阶微分方程边值问题正解的存在性[J]. 湖南师范大学自然科学学报, 2012,35(5):914.
[9] BAI Z. Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. J Math Anal Appl, 2005,311(2):495505.
[10] GE W. The existence of solutions of m-point boundary value problems at resonance[J]. Acta Math Appl Sin, 2005,28(4):288295.
[11] CHENG L, LIU W, YE Q. Boundary value problem for a coupled system of fractional differential equations with p-Laplacian operator at resonance[J]. Electr J Diff Equ, 2014(60):112.
[12] BAI Z. On positive solutions of nonlocal fractional boundary value problem[J]. Nonlinear Anal: TMA, 2010,72(2):916924.
[13] CHEN T. An antiperiodic boundary value problem for the fractional differential equation with p-Laplacian operator[J]. Appl Math, 2012,25(11):16711675.
[14] BAI Z. Solvability for a class of fractional mpoint boundary value problems at resonance[J]. Comput Math Appl, 2012,62(3):12921302.
[15] 钟成奎.非线性泛函分析引论[M].兰州:兰州大学出版社,1998.
(编辑 HWJ)
总结:本文关于微分方程论文范文,可以做为相关论文参考文献,与写作提纲思路参考。
参考文献:
1、 带p—Laplacian算子三阶微分方程边值问题正解存在性 摘要:许多不同应用数学和物理领域的研究都可归结为带有pLaplacian算子的边值问题,因此对此问题的研究具有重要的理论意义和应用价值。本文讨论。
2、 分数阶脉冲微分方程边值问题解存在性 摘要:为了解决对半无穷区间上具有可数个脉冲点且带有积分边界条件的分数阶脉冲微分方程边值问题,具体研究此类微分方程边值问题解的存在性。通过定义合适。
3、 无穷区间上含有p—Laplacian算子n阶积分边值问题正解存在性 摘要:运用Leray-Schauder非线性抉择定理研究了一类无穷区间上含有p-Laplacian算子的n阶微分方程积分边值问题:(φp(x(。
4、 具有pLaplacian算子共振微分方程组解存在性 摘要:为了研究具有非线性分数阶微分算子的微分方程共振边值问题解的存在性,引入了推广的Mawhin 连续定理,通过定义合适的Banach空间及范数。
5、 基于模糊RBF神经网络分数阶滑模控制器优化设计 摘 要: 针对神经滑模控制系统中存在的对先验数据依赖性较强的问题,结合RBF神经网络的泛化能力和自学习能力以及模糊推理算法的强适应能力,提出基于。
6、 上覆分数阶粘弹性饱和场地土位移地震放大系数 摘要:考虑土体液相和固相的耦合作用,将基岩上覆场地土视为两相饱和多孔介质。为了考虑饱和场地土的粘弹性特性,其固相土骨架的应力应变关系利用分数阶K。