一类p-Laplace分数阶脉冲常微分系统解的存在性
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摘要
本文利用山路引理研究一类p-Laplace分数阶脉冲常微分系统解的存在性问题.在非线性项满足超p次增长的条件下,证明系统至少有一个非平凡解.
In this paper we investigate the existence of solutions to a class of p-Laplace fractional impulsive ordinary differential system.By using the mountain pass theorem,we show that the system has at least one nontrivial solution if its nonlinear term possesses a super-p-growth rate.
In this paper we investigate the existence of solutions to a class of p-Laplace fractional impulsive ordinary differential system.By using the mountain pass theorem,we show that the system has at least one nontrivial solution if its nonlinear term possesses a super-p-growth rate.
引文
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[2]Podlubny I.Fractional differential equations[M].Mathematics in Science and Engineering,1999.
[3]Jin H.,Liu W.On the periodic boundary value problem for Duffing type fractional differential equation with p-Laplacian operator[J].Boundary Value Problems,2015,2015(1):144-154.
[4]Hu Z.,Liu W.,Rui W.Periodic boundary value problem for fractional differential equation[J].International Journal of Mathematics,2012,23(10),57-224.
[5]Wang G.,Baleanu D,Zhang L.Monotone iterative method for a class of nonlinear fractional differential equations[J].Fractional Calculus&Applied Analysis,2012,15(2),244-252.
[6]Bai Z.,Zhang S.,Sun S.,et al.Monotone iterative method for fractional differential equations[J].Electronic Journal of Differential Equations,2016,2016(6):1-8.
[7]Bai Z.,LüH.Positive solution for boundary value problem of nonlinear differential equation[J].Journal of Mathematical Analysis&Applications,2005,311(2),495-505.
[8]Mawhin J.,Willem M.Critical point theory and Hamiltonian systems[M].New York:Springer-Verlag,1989.
[9]Wang Y.,Li Y.,Zhou J.Solvability of boundary value problems for impulsive fractional differential equations via critical point theory[J].Mediterranean Journal of Mathematics,2016,13(6),1-22.
[10]Chen T.,Liu W.Solvability of fractional boundary value problem with p-Laplacian via critical point theory[J].Boundary Value Problems,2016,2016(1):75-86.
[11]Zhao Y.,Chen H.,Qin B.Multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods[J].Applied Mathematics&Computation,2015,257(C),417-427.
[12]Tian Y.,Nieto J J.The applications of critical-point theory to discontinuous fractional-order differential equations[J].Proceedings of the Edinburgh Mathematical Society,2017,60(4),1-31.
[13]Bonanno,G,Rodriguez-López,R,Tersian S.Existence of solutions to boundary value problem for impulsive fractional differential equations[J].Fractional Calculus&Applied Analysis,2014,17(3),717-744.
[14]Rodríguez-López R.,Tersian S.Multiple solutions to boundary value problem for impulsive fractional differential equations[J].Fractional Calculus&Applied Analysis,2014,17(4),1016-1038.
[15]Averna D.,Tersian S.,Tornatore E.On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations[J].Fractional Calculus&Applied Analysis,2016,19(1):253-266.
[16]Zhao Y.,Tang L.Multiplicity results for impulsive fractional differential equations with p-Laplacian via variational methods[J].Boundary Value Problems,2017,2017(1):123-137.
[17]Xie J.,Zhang X.Infinitely many solutions for a class of fractional impulsive coupled systems with(p,q)-Laplacian[J].Discrete Dynamics in Nature and Society,2018,2018(1):1-14.
[18]Tang C.L.,Wu X.P..Periodic solutions for a class of new superquadratic second order Hamiltonian systems[J].Applied Mathematics Letters,2014,34(2),65-71.
[19]Kilbas A.A.,Srivastava H.M.,Trujillo J.J.Theory and applications of fractional differential equations[M].Netherlands:Elsevier,2006.
[20]Zhou Y.Basic theory of fractional differential equations[M].World Scientific.Singapore,2014.
[21]Jiao F.,Zhou Y.Existence of solutions for a class of fractional boundary value problems via critical point theory[J].Computers&Mathematics with Applications,2011,62(3),1181-1199.
[22]Rabinowitz P.H.Minimax methods in critical point theory with applications to differential equations[M].Providence:American Mathematical Society,1986.
[23]Bartolo P.,Benci V.,Fortunato D.Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity[J].Nonlinear Analysis,1983,7,241-273.