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非线性半正分数阶微分方程多重正解的存在性 被引量：2

Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations
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摘要 应用Krasnoselskii不动点定理研究了分数阶微分方程的多重正解的存在性。D0α+u(t)=p(t)f(t,u(t))-q(t),0<t<1,u(0)=u(1)=u′(0)=u′(1)=0。其中3<α≤4是任意实数,D0α+是标准的Riemann-Liouville型分数阶微分。 The existence of multiple positive solutions of an fractional differential equation of the form Dα0＋u（t）=p（t）f（t,u（t））-q（t）,0t1,u（0）=u（1）=u＇（0）=u＇（1）=0, are obtained,where 3α≤4 is a real number,and Dα0＋ is the standard Riemann-Liouville differentiation.The proof relies on Krasnoselskii＇s fixed point theorem.
作者 许晓婕
机构地区 中国石油大学(华东)
出处 《科学技术与工程》 2010年第35期8653-8656,8662,共5页 Science Technology and Engineering
关键词 正解 分数阶微分方程 半正边值问题 锥不动点定理 positive solutions fractional differential equation semipositone boundary value problemskrasnoselskii＇s fixed point theorem
分类号 O175.8 [理学—基础数学]
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参考文献8

  • 1Anatoly K A,Hari S H,Juan T J.Theory and applications of fractional differential equations.North-Holland Mathematics studies,204,Amsterdam;Elsevier Science B.V.,2006.
  • 2Oldham K B,Spanier J.The fractional calculus.New York and London; Academic Pree,1974.
  • 3Ross B(ED.).The fractional calculus and its applications.Lecture Notes in Mathematics 475,Berlin,Springer-Verlag,1975.
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  • 6Bai Z,Lu H.Positive solutions for boundary value problem of nonlinear fractional differential equation,J Math Anal Appl,2005;311:495-505.
  • 7Xu X,Jiang D,Yuan C.Multiple positive solutions for boundary value problem of nonlinear fractional differential equation.Nonlinear Analysis Series A:Theory,Methods and Applications,Nonlinear Analysis,2009;71:4676-4688.
  • 8Krasnoselskii M A.Positive solutions of operator equations.Noordhoff,Groningen,1964.

同被引文献17

  • 1高雷阜,王金希,吴洪涛.Banach空间中一类变分包含解的存在性和唯一性[J].辽宁工程技术大学学报（自然科学版）,2012,31(2):252-255. 被引量：8
  • 2任建娅,尹建华,耿万海.小波方法求一类变系数分数阶微分方程数值解[J].辽宁工程技术大学学报（自然科学版）,2012,31(6):925-928. 被引量：12
  • 3郭大钧.非线性泛函分析.济南:山东科学技术出版社,2004.
  • 4A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B. V. , Amsterdam, The Netherlands, 2006.
  • 5Z. B, Bai, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal. 72, (2010) 916 -924.
  • 6Xiaojie Xu , Xiangli Fei,The positive properties of Green's function for three point boundaryvalue problems of nonlinear fractional differential equations and its applications, Commun Nonlinear Sci Numer Simulat 17 (2012)1555 -1565.
  • 7Xiaojie Xu, Multiple positive solutions to singular positone and semipositone boundary value problems of nonlin- ear fractional differential equations, Mathematics Subject Clssification, (2000) 34B15.
  • 8Xiangkui Zhao, Positive solutions for four - point boundary valueproblems , Commun Nonlinear Sci Number Simu- lat ( 2011 ), doi : 10.1016/j. cnsns. 2011.01. 002.
  • 9] Xiaojie Xu, Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equa- tion, Nonlinear Analysis, 71 ( 2009 ) ,4676 - 4688.
  • 10Ravi P. Agarwal, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations, J. Math. Anal. Appl, 371 ( 2010 ) ,57 - 68.

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科学技术与工程
2010年 第35期

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