JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (4): 22-28.doi: 10.6040/j.issn.1671-9352.0.2018.279

Previous Articles     Next Articles

Applications of variational method to impulsive differential systems with variable exponent

ZHANG Shen-gui   

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Published:2019-04-08

PDF (PC)

370

Abstract: By using variational method, a class of impulsive differential systems with variable exponent and nonlocal coefficient are investigated. When the nonlinearity has a sublinear growth near zero, some results for existence of multiple periodic solutions are obtained via a variant Clarks theorem.

Key words: periodic solution, p(t)-Laplacian operator, Kirchhoff problem, impulsive effects, critical point

CLC Number: 

  • O175.12
[1] NIETO J J, RODRIGUEZ-LOPEZ R. New comparison results for impulsive integro-differential equations and applications[J]. J Math Anal Appl, 2007, 328(2):1343-1368.
[2] NIETO J J, OREGAN D. Variational approach to impulsive differential equations[J]. Nonlinear Anal, 2009, 10(2):680-690.
[3] NIETO J J. Variational formulation of a damped Dirichlet impulsive problem[J]. Applied Mathematics Letters, 2010, 23(8):940-942.
[4] TIAN Yu, GE Weigao. Applications of variational methods to boundary value problem for impulsive differential equations[J]. Proceedings of the Edinburgh Mathematical Society, 2008, 51(1):509-527.
[5] ZHOU Jianwei, LI Yongkun. Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects J]. Nonlinear Anal, 2010, 72(8):1594-1603.
[6] 毛安民, 张琳. 变分方法对一类p阶超线性脉冲微分方程的应用[J].中国科学(数学), 2016, 46(12):1845-1862. MAO Anmin, ZHANG Lin. Applications of variational method to impulsive p-Laplacian problem with superlinear impulses[J]. Scisin Math, 2016, 46(12):1845-1862.
[7] ZHIKOV V. On some variational problems[J]. Russian J Math Phys, 1997, 5(1):105-116.
[8] RUZICKA M. Electrorheologial fluids: modeling and mathematial theory[M]. Berlin: Springer-Verlag, 2000.
[9] CHEN Y, LEVINE S, RAO M. Variable exponent, linear growth functionals in image restoration[J]. SIAM J Appl Math, 2006, 66(4):1383-1406.
[10] FAN Xianling, FAN Xing. A Knobloch-type result for p(t)-Laplacian systems[J]. J Math Anal Appl, 2003, 282(1):453-464.
[11] WANG Xianjun, YUAN Ruan. Existence of periodic solutions for p(t)-Laplacian systems[J]. Nonlinear Anal, 2009, 70(2):866-880.
[12] ZHANG Ziheng, XIANG Tian, YUAN Ruan. Homoclinic solutions for p(t)-Laplacian-Hamiltonian systems without coercive conditions[J]. Mediterranean Journal of Mathematics, 2016, 13(4):1589-1611.
[13] ZHANG Ziheng, YUAN Ruan. Existence of two almost homoclinic solutions for p(t)-Laplacian Hamiltonian systems with a small perturbation[J]. Journal of Applied Mathematics and Computing, 2016, 52(1):173-189.
[14] AN Yukun, RU Yuanfang, WANG Fanglei. Existence of nonconstant periodic solutions for a class of second-order systems with p(t)-Laplacian[J]. Boundary Value Problems, 2017, 170(1):1-15.
[15] 张申贵, 慕嘉. 非自治p(t)拉普拉斯系统周期解的存在性[J]. 数学杂志,2017,37(2):409-418. ZHANG Shengui, MU Jia. Existence of periodic solutions for non-autonomous p(t)-Laplacian systems[J]. Journal of Mathematics, 2017, 37(2):409-418.
[16] LIU Zhaoli, WANG Zhiqiang. On Clarks theorem and its applications to partially sublinear problems[J]. Ann I H Poincare AN, 2015, 32(5):1015-1037.
[1] ZHANG Huan, LI Yong-xiang. Positive periodic solutions of higher-order ordinary differential equations with delayed derivative terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(4): 29-36.
[2] WU Yi-jia, CHENG Rong. Infinitely many nontrival solutions for a class of Schrödinger equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 84-88.
[3] LI Le-le, JIA Jian-wen. Hopf bifurcation of a SIRC epidemic model with delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(1): 116-126.
[4] CHEN Yu-jia, YANG He. Existence of periodic solutions of a class of third order delay differential equations in Banach spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 84-94.
[5] ZHANG Shen-gui. Multiple solutions of Navier boundary value problem for fourth-order elliptic equation with variable exponents [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 32-37.
[6] ZHANG Di, LIU Wen-bin. Existence of solutions for p(t)-Laplacian fractional infinite-point boundary value problems at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 72-80.
[7] . Periodic solutions for second order singular damped differential equations with a weak singularity [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 84-88.
[8] WANG Shuang-ming. Dynamical analysis of a class of periodic epidemic model with delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(1): 81-87.
[9] CHEN Bin. Third-order periodic boundary value problems with sign-changing Greens function [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 79-83.
[10] JIANG Jing, GAO Qing-ling, ZHANG Ke-yu. Existence of weak solutions for a second order Dirichlet boundary value problem on time scales [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 99-103.
[11] . Existence of periodic solutions for a class of Hamiltonian systems with p-Laplace [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 42-46.
[12] ZHANG Shen-gui. Multiplicity of solutions for Kirchhoff type equation involving the p(x)-biharnonic operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 48-53.
[13] WU Cheng-ming. Existence of positive periodic solutions for second order singular coupled systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 81-88.
[14] XU Man. Existence of positive periodic solutions of impulsive functional differential equations with two parameters [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 69-74.
[15] SUN Guo-wei, MAI A-li. Multiple homoclinic solutions for second order nonlinear difference equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 51-54.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] LIU Fang-yuan, MENG Xian-jia, TANG Zhan-yong, FANG Ding-yi, GONG Xiao-qing. Android application protection based on smali code obfuscation[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(3): 44 -50 .
[2] LIAO Xiang-wen, ZHANG Ling-ying, WEI Jing-jing, GUI Lin, CHENG Xue-qi, CHEN Guo-long. User influence analysis of social media with temporal characteristics[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(3): 1 -12 .
[3] GU Shen-ming, LU Jin-lu, WU Wei-zhi, ZHUANG Yu-bin. Local optimal granularity selections in generalized multi-scale decision systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 1 -8 .
[4] ZHU Lin. Separated monic representations of quivers of type A4and RSS equivalences[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 1 -8 .
[5] . Interval algorithm for mixed integer nonlinear two-level programming problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 9 -17 .
[6] YAN Yan, HAO Xiao-hong. Differential privacy partitioning algorithm based on adaptive density grids[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(9): 12 -22 .
[7] YE Xiao-ming, CHEN Xing-shu, YANG Li, WANG Wen-xian, ZHU Yi, SHAO Guo-lin, LIANG Gang. Anomaly detection model of host group based on graph-evolution events[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(9): 1 -11 .
[8] Zhao-xia WU,Jia-qi WANG. Wireless single spectrum secure auction algorithm[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(11): 51 -55 .
[9] WAN Peng-fei, GAO Xing-bao. Novel artificial bee colony algorithm based on objective space decomposition for solving multi-objective optimization problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(11): 56 -66 .
[10] SHAO Yong. Semilattice-ordered completely regular periodic semigroups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 1 -5 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd