JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 1-6.doi: 10.6040/j.issn.1671-9352.0.2018.131

   

Periodic solutions for a class of Kirchhoff-type differential systems

ZHANG Shen-gui   

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Published:2019-10-12

PDF (PC)

449

Abstract: By using variational principle, the author studied periodic solutions for a class of superlinear Kirchhoff-type p(t)-Laplacian systems. Under the condition of no Ambrosetti-Rabinowitz-type growth, some results for the existence of periodic solutions are obtained by means of a variant mountain pass type theorem.

Key words: Kirchhoff-type equation, p(t)-Laplacian systems, periodic solutions, critical point, mountain pass thoerem

CLC Number: 

  • O175.12
[1] ZHIKOV V. On some variational problems[J]. Russian J Math Phys, 1997, 5(1):105-116.
[2] RUZICKA M. Electrorheologial fluids: modeling and mathematial theory[M]. Berlin: Springer-Verlag, 2000.
[3] CHEN Y, LEVINE S, RAO M. Variable exponent, linear growth functionals in image restoration[J]. SIAM J Appl Math, 2006, 66(4):1383-1406.
[4] FAN Xianling, FAN Xing. A Knobloch-type result for p(t)-Laplacian systems[J]. J Math Anal Appl, 2003, 282(2):453-464.
[5] WANG Xianjun, YUAN Ruan. Existence of periodic solutions for p(t)-Laplacian systems[J]. Nonlinear Analysis, 2009, 70(2):866-880.
[6] ZHANG Liang, TANG Xianhua, CHEN Jing. Infinitely many periodic solutions for some second-order differential systems with p(t)-Laplacian[J]. Boundary Value Problems, 2011, 33(1):1-15.
[7] CHEN Peng, TANG Xianhua, AGARWAL R. Infinitely many homoclinic solutions for nonautonomous p(t)-Laplacian Hamiltonian systems[J]. Computer and Mathematical with Applications, 2012, 63(4):751-763.
[8] PASCA D, TANG Chunlei. Periodic solutions of non-autonomous second order systems with(q(t), p(t))-Laplacian[J]. Mathematica Slovaca, 2014, 64(1):913-930.
[9] 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.
[10] 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.
[11] AUTUORI G, PUCCI P, SALVATORI M C. Asymptotic stability for anisotropic Kirchhoff systems[J]. J Math Anal Appl, 2009, 352(1):149-165.
[12] BONANNO G. Relations between the mountain pass theorem and local minima[J]. Advance Nonlinear Analysis, 2012, 1(3):205-220.
[1] ZHANG Shen-gui. Applications of variational method to impulsive differential systems with variable exponent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(4): 22-28.
[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] 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.
[4] . 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.
[5] 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.
[6] 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.
[7] . 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.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] ZHANG Shen-gui. Multiplicity of solutions for local superlinear p-kirchhoff-type equation#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(05): 61-68.
[13] ZHANG Guo-wei 1, CHEN Ang2. Infinitely connectivity of the wandering domain of#br# Baker’s original example [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 70-73.
[14] GUO Ying. Pseudo almost solutions of difference equations [J]. J4, 2012, 47(2): 42-46.
[15] ZHANG Shen-gui. Infinitely many solutions for a class of superlinear p(x)-biharmonic equation [J]. J4, 2012, 47(10): 116-120.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd