YANG Fei,CHEN Guoping. Solutions for Impulsive FractionalOrder Differential Equations Based on Critical Point Theorem[J]. Journal of Jishou University(Natural Sciences Edition), DOI: 10.3969/j.cnki.jdxb.2016.03.004.
[1] AGARWAL RAVI P,AHMAD BASHIR.Existence Theory for Anti-Periodic Boundary Value Problems of Fractional Differential Equations and Inclusions[J].Computers and Mathematics with Applications,2011,62(3):1 200-1 214.
[2] TARASOV VASILY E.Fractional Dynamics:Applications of Fractional Calculus to Dynamics of Particles,Fields and Media[M].北京:高等教育出版社,2011:89-112
[3] WANG Jinrong,ZHOU Yong,FECKAN MICHAL.Nonlinear Impulsive Problems for Fractional Differential Equations and ULam Stability[J].Computers and Mathematics with Applications,2012,64(10):3 389-3 405.
[4] GUO Tianliang,JIANG Wei.Impulsive Problems for Fractional Differential Equations with Boundary Value Conditions[J].Computers and Mathematics with Applications,2012,64:3 281-3 291.
[5] CHEN Yi,TANG Xianhua.Solvability of Sequential Fractional Order Multi-Point Boundary Value Problems at Resonance[J].Applied Mathematics and Computation,2012,218:7 638-7 648.
[6] KILBAS ANATOLY A,SRIVASTAVA HARI M,TRUJILLO JUAN J.Theory and Applications of Fractional Differential Equations[M]∥Noorth-Holland Mathematics Studies.Amsterdam:Elsevier Science Ltd.,2006:105-146.
[7] ZHANG Ziheng,YUAN Rong.An Application of Variational Methods to Dirichlet Boundary Value Problem with Impulses[J].Nonlinear Analysis:Real World Applications,2010,11:155-162.
[8] JIAO Feng,ZHOU Yong.Existence of Solutions for a Class of Fractional Boundary Value Problems via Critical Point Theory[J].Computers and Mathematics with Applications,2011,62.
[9] JIA Mei,LIU Xiping.Multiplicity of Solutions for Integral Boundary Value Problems of Fractional Differential Equations with Upper and Lower Solutions[J].Applied Mathematics and Computation,204,232(1):313-323.
[10] JIAO Feng,ZHOU Yong.Existence Results For Fractional Boundary Value Problem var Critical Point Theory[J].International Journal of Bifurcation and Chaos,2012,22(4).
[11] ZHANG Quanguo,SUN Hongrui,LI Yaning.Existence of Solution for a Fractional Advection Dispersion Equation in 〖WTHZ〗R〖WTBZ〗n[J].Applied Mathematical Modelling,2014,38:4 062-4 075.
[12] SUN Hongrui,ZHANG Quanguo.Existence of Solutions for a Fractional Boundary Value Problem via the Mountain Pass Method and an Iterative Technique[J].Computers and Mathematics with Applications,2012,64:3 436-3 443.
[13] XIE Wenzhe,XIAO Jing,LUO Zhiguo.Existence of Solutions for Fractional Boundary Value Problem with Nonlinear Derivative Dependence[J].Abstract and Applied Analysis,2014,Article ID 812910,8 Pages:1-8.
[14] CHEN Jing,TANG X H.Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory[J].Abstract and Applied Analysis,2012,Article ID 648635,21 Pages:1-21.
[15] BIN Ge.Multiple Solutions for a Class of Fractional Boundary Value Problems[J].Abstract and Applied Analysis,2012,Article ID 468980,16 Pages:1-16.
[16] NEMAT NYAMORADI.Infinitely Many Solutions for a Class of Fractional Boundary Value Problems with Dirichlet Boundary Conditions[J].Mediterranean Journal Mathematics,2014,11(1):75-87.
[17] GABRIELE BONANNO,ROSANA RODRGUEZ-LPEZ,STEPAN TERSIAN.Multiple Solutions to Boundary Value Problem for Impulsive Fractional Differential Equations[J].Fractional Calculus and Applied Analysis,2014,17(3):1 016-1 038.
[18] NEMAT NYAMORADI,ROSANA RODRGUEZ-LPEZ.On Boundary Value Problems for Impulsive Fractional Differential Equations[J].Applied Mathmatics and Computation,2015,271:874-892.
[19] RABINOWITZ PAUL H.Minimax Methods in Critical Point Theory with Applications to Differential Equations[M].American:American Mathmatical Society,1986:5-6.
[20] NIETO JUAN J,O’REGAN DONAL.Variational Approach to Impulsive Differential Equations[J].Nonlinear Analysis:Real World Applications,2009,10(2):680-690.