| [1] | Ambrosetti A, Rabinowitz P H. Dual variational methods in critical point theory and applications. J Funct Anal, 1973, 14(4): 349-381 |
| [2] | Bai L, Dai B X. Three solutions for a p-Laplacian boundary value problem with impulsive effects. Appl Math Comput, 2011, 217(24): 9895-9904 |
| [3] | Bai L, Nieto J J. Variational approach to differential matrixs with not instantaneous impulses. Appl Math Lett, 2017, 73: 44-48 |
| [4] | Chen H W, He Z M, Li J L. Multiplicity of solutions for impulsive differential matrix on the half-line via variational methods. Bound Value, 2016, 2016: Article number 14 |
| [5] | Fang F, Liu S B. Nontrivial solutions of superlinear p-Laplacian matrixs. J Math Anal Appl, 2009, 351(1): 138-146 |
| [6] | Jeanjean L. On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer-type problem set on RN. Proc R Soc Edinb Sect A-Math, 1999, 129(4): 787-809 |
| [7] | Liu J, Zhao Z Q. An application of variational methods to second-order impulsive differential matrix with derivative dependence. Electron J Differ Equ, 2014, 2014(62): 1-13 |
| [8] | 刘健, 赵增勤. Cerami 条件下脉冲边值问题古典解的存在性. 数学学报, 2016, 59(5): 609-622 |
| [8] | Liu J, Zhao Z Q. Existence of classical solutions to impulsive boundary value problems under Cerami condition. Acta Math Sinica (Chin Ser), 2016, 59(5): 609-622 |
| [9] | 刘健, 赵增勤, 于文广. 具非自治微小扰动的脉冲方程三个古典解的存在性. 数学学报, 2019, 62(3): 441-448 |
| [9] | Liu J, Zhao Z Q, Yu W G. The existence of triple classical solutions to impulsive problems with small non-autonomous perturbations. Acta Math Sinica (Chin Ser), 2019, 62(3): 441-448 |
| [10] | Liu S B. On superlinear problems without the Ambrosetti and Rabinowitz condition. Nonlinear Anal, 2010, 73(3): 788-795 |
| [11] | 刘轼波, 李树杰. 一类超线性椭圆方程的无穷多解. 数学学报, 2003, 46(4): 625-630 |
| [11] | Liu S B, Li S J. Infinitely many solutions for superlinear elliptic matrix. Acta Math Sinica (Chin Ser), 2003, 46(4): 625-630 |
| [12] | Menasria L, Bouali T, Guefaifia R, Biomy M. Existence of weak solutions for p-Laplacian problem with impulsive effects. Appl Sci, 2020, 22: 128-145 |
| [13] | Miyagaki O H, Souto M A S. Superlinear problems without Ambrosetti and Rabinowitz growth condition. J Differ Equ, 2008, 245(12): 3628-3638 |
| [14] | Nieto J J. Variational formulation of a damped Dirichlet impulsive problem. Appl Math Lett, 2010, 23(8): 940-942 |
| [15] | Nieto J J, O'Regan D. Variational approach to impulsive differential matrixs. Nonlinear Anal: RWA, 2009, 10(2): 680-690 |
| [16] | Qian A X. Existence of infinitely many nodal solutions for a superlinear Neumann boundary value problem. Bound Value Probl, 2005, 2005: Article number 3 |
| [17] | Shi H X, Chen H B, Zhang Q. Infinitely many solutions for a p-Laplacian boundary value problem with impulsive effects. J Appl Math Comput, 2014, 46(1): 93-106 |
| [18] | Tian Y, Ge W G. Applications of variational methods to boundary-value problem for impulsive differential matrixs. Proc Edinb Math Soc, 2008, 51(2): 509-527 |
| [19] | Willem M. Minimax Theorems. Boston: Birkh?user Boston Inc, 1996 |
| [20] | Xu J F, Wei Z L, Ding Y Z. Existence of weak solutions for p-Laplacian problem with impulsive effects. Taiwan J Math, 2013, 17(2): 501-515 |
| [21] | Zeng Y H, Xie J L. Three solutions to impulsive differential matrixs involving p-Laplacian. Adv Differ Equ, 2015, 2015(1): 1-10 |
| [22] | Zhang Z H, Yuan R. An application of variational methods to Dirichlet boundary value problem with impulses. Nonlinear Anal: RWA, 2010, 11(1): 155-162 |
| [23] | 赵俊峰. Banach 空间结构理论. 武汉: 武汉大学出版社, 1991 |
| [23] | Zhao J F. Stucture Theory for Banach Space. Wuhan: Wuhan University Press, 1991 |
| [24] | Zhou J W, Li Y K. Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects. Nonlinear Anal: TMA, 2009, 71(7/8): 2856-2865 |