Existence and multiplicity of weak solutions for a nonlinear impulsive (q, p)-Laplacian dynamical system

被引：0
|
作者：
Yang, Xiaoxia [1 ]
机构：
[1] Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2017年
基金：
中国国家自然科学基金;
关键词：
(q; p)-Laplacian; existence; multiplicity; nontrivial solution; variational methods; 2ND-ORDER DIFFERENTIAL-SYSTEMS; PERIODIC-SOLUTIONS;
D O I：
10.1186/s13662-017-1145-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the existence and multiplicity of nontrivial weak solutions for a class of nonlinear impulsive (q, p)-Laplacian dynamical systems. The key contributions of this paper lie in (i) Exploiting the least action principle, we deduce that the system we are interested in has at least one weak solution if the potential function has sub-(q, p) growth or (q, p) growth; (ii) Employing a critical point theorem due to Ding (Nonlinear Anal. 25(11): 1095-1113, 1995), we derive that the system involved has infinitely many weak solutions provided that the potential function is even.
引用
收藏
页数：12
相关论文
共 50 条
  • [1] On critical exponent for the existence and multiplicity of positive weak solutions for a class of (p, q)-Laplacian nonlinear system
    Ghaemi, M. B.
    Afrouzi, G. A.
    Rasouli, S. H.
    Choubin, M.
    JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2011, 3 (04): : 432 - 439
  • [2] Periodic solutions for a nonlinear (q,p)-Laplacian dynamical system with impulsive effects
    Xiaoxia Yang
    Haibo Chen
    Yang, X. (yangxiaoxia0731@gmail.com), 1600, Springer Verlag (40): : 1 - 2
  • [3] Existence of positive weak solutions for (p, q)-Laplacian nonlinear systems
    SAMIRA ALA
    G A AFROUZI
    A NIKNAM
    Proceedings - Mathematical Sciences, 2015, 125 : 537 - 544
  • [4] Existence of positive weak solutions for (p, q)-Laplacian nonlinear systems
    Ala, Samira
    Afrouzi, G. A.
    Niknam, A.
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2015, 125 (04): : 537 - 544
  • [5] EXISTENCE AND MULTIPLICITY OF POSITIVE WEAK SOLUTIONS FOR A NEW CLASS OF (P; Q)-LAPLACIAN SYSTEMS
    Guefaifia, Rafik
    Boulaaras, Salah
    Zuo, Jiabin
    Agarwal, Praveen
    MISKOLC MATHEMATICAL NOTES, 2020, 21 (02) : 861 - 872
  • [6] Maximum Principle and Existence of Weak Solutions for Nonlinear System Involving Weighted (p, q)-Laplacian
    Khafagy, Salah. A.
    Herzallah, Mohamed A. E.
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2016, 40 (03) : 353 - 364
  • [7] Existence and Multiplicity of Nontrivial Solutions for a (p, q)-Laplacian System on Locally Finite Graphs
    Yang, Ping
    Zhang, Xingyong
    TAIWANESE JOURNAL OF MATHEMATICS, 2024, 28 (03): : 551 - 588
  • [8] EXISTENCE OF WEAK SOLUTIONS FOR p-LAPLACIAN PROBLEM WITH IMPULSIVE EFFECTS
    Xu, Jiafa
    Wei, Zhongli
    Ding, Youzheng
    TAIWANESE JOURNAL OF MATHEMATICS, 2013, 17 (02): : 501 - 515
  • [9] Existence of periodic solutions for sublinear second order dynamical system with (q, p)-Laplacian
    Yang, Xiaoxia
    Chen, Haibo
    MATHEMATICA SLOVACA, 2013, 63 (04) : 799 - 816
  • [10] Existence and multiplicity of weak solutions for eigenvalue Robin problem with weighted p(.)-Laplacian
    Aydin, Ismail
    Unal, Cihan
    RICERCHE DI MATEMATICA, 2023, 72 (02) : 511 - 528
12345