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一类分数阶Laplacian方程边值问题解的存在性与唯一性 被引量：3

Existence and uniqueness of the solutions to a boundaryvalue problem for a class of fractional differentialequations with p-Laplace operator
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摘要 研究了一类分数阶p-Laplacian方程2点边值问题解的存在性,利用Leray-Schauder非线性抉择和Banach压缩映射原理获得了该边值问题解存在性和唯一性的充分条件,得到了一些新的结果. The class of fractional differential equation with a two - point boundary value problem and p - Laplace operator is studied. By using the Leray - Schauder nonlinear alternative theorem and Banach contraction mapping principle, some sufficient conditions concerning the existence and uniqueness of solutions for this boundary value problem are obtained. Some known results are extended and improved.
作者 郑春华 宁艳艳
机构地区 陕西工业职业技术学院基础部
出处 《云南民族大学学报（自然科学版）》 CAS 2014年第6期429-433,共5页 Journal of Yunnan Minzu University:Natural Sciences Edition
基金 国家自然科学基金(11271364) 陕西工业职业技术学院科研项目(ZK13-40)
关键词 分数阶微分方程 P-LAPLACE算子 两点边值问题 LERAY-SCHAUDER非线性抉择 BANACH压缩映射原理 fractioal order differential equation p - Laplace operator two - point boundary value problem Leray -Schauder nonlinear alternative theorem Banach contraction mapping principle
分类号 O175.8 [理学—基础数学]
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参考文献10

  • 1MILLER K S,ROSS B.An introduction to the fractional calculus and fractional differential equations[M].New York:Wiley,1993.
  • 2PODLUBNY I.Fractional differential equation[M].San Diego:Academic Press,1999.
  • 3KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and applications of fractional differential equations[M].Netherlands:Elsevier,2006.
  • 4BAI Zhan-bing,LYU Hai-shen.Positive solutions of boundary value problems of nonlinear fractional differential equation[J].Journal of Mathematical Analysis and Applications,2005,311(2):495-505.
  • 5ZHANG Shu-qin.Positive solutions for boundary value problems of nonlinear fractional differential equations[J].Electronic Journal of Differential Equations,2006(36):1-12.
  • 6ZHAO Yi-ge,SUN Shu-rong,HAN Zhen-lai.Positive solutions for boundary value problems of nonlinear fractional differential equations[J].Applied Mathematics and Computation,2011,217(16):6950-6958.
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  • 9JIANG Wei-hua.Eigenvalue interval for multi-point boundary value problems of fractional differential equations[J].Journal of Applied Mathematic and Computing,2013,219(9):4570-4575.
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同被引文献18

  • 1MILLER K S, ROSS B. An introduction to the fractional calculus and fractional differential equations[M] . New Y ork: Wiley,1993.
  • 2PODLUBNY I. Fractional differential equation[M]. San Diego: Academic Press, 1999.
  • 3KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Netherlands :Elsevier B V,2006.
  • 4BAI Zhan-bing, LYU Hai-Shen. Positive solutions of boundary value problems of nonlinear fractional differential equation[J] . JMath Anal A ppl,2005(311) :495 -5 0 5 .
  • 5ZHAO Yi-ge, SUN Shu-rong, HAN Zhen-lai. Positive solutions for boundary value problems of nonlinear fractional differential equations[J]. Applied Mathematics and Computation, 2011,217 (1 6 ) :6950 -6 958 .
  • 6CHEN Tai-yong, LIU Wen-bin, HU Zhi-gang. A boundary value problem for fractional differential equation with p - Laplacianoperator at resonance[J]. Nonlinear Anal, 2 0 1 2 ,7 5 (6 ) :3210 -3 217 .
  • 7BAI Zhan-bing. On positive solutions of a nonlocal fractional boundary value pro blem [J]. Nonlinear Analysis, 2010,72 ( 2 ) :916 -9 2 4 .
  • 8LI Cheng-fu, LUO Xian-nan, ZHOU Yong. Existence of positive solutions of the boundary value problem for nonlinear fractionaldifferential equations[J]. Computers & Mathematics with Applications, 2010, 5 9 (3 ) : 1363 -1 3 7 5 .
  • 9ZHANG Ying-han, BAI Zhan-bing. Existence of solutions for nonlinear fractional three - point boundary value problems at resona n c e [J]. J Appl Math Comput, 2011, 3 6 (1 /2 ) :417 -4 4 0 .
  • 10LI Xiao-yan, LIU Song, JIANG Wei. Positive solutions for boundary value problem of nonlinear fractional functional differentialequations[J]. Applied Mathematics and Computation, 2011,217 (2 2 ) :9278 -9 2 8 5 .

引证文献3

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云南民族大学学报（自然科学版）
2014年 第6期

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