Articles

EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN

  • GE Bin ,
  • XUE Xiao-Ping ,
  • ZHOU Qiang-Mei
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  • Department of Applied Mathematics, Harbin Engineering University, Harbin 150001, China; Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China; Library, Northeast Forestry University, Harbin 150040, China

Received date: 2010-05-12

  Revised date: 2010-09-05

  Online published: 2011-09-20

Supported by

This work was supported by the National Science Foun-dation of China (11001063, 10971043), the Fundamental Research Funds for the Central Universities (HEUCF20111134), China Postdoctoral Science Foundation Funded Project (20110491032), Heilongjiang Provincial Sci-ence Foundation for Distinguished Young Scholars (JC200810), Program of Excellent Team in Harbin Institute of Technology and the Natural Science Foundation of Heilongjiang Province (A200803).

Cite this article

GE Bin , XUE Xiao-Ping , ZHOU Qiang-Mei . EXISTENCE OF PERIODIC SOLUTIONS FOR A DIFFERENTIAL INCLUSION SYSTEMS INVOLVING THE p(t)-LAPLACIAN[J]. Acta mathematica scientia, Series B, 2011 , 31(5) : 1786 -1802 . DOI: 10.1016/S0252-9602(11)60361-5

References

[1] Zhikov V V. Averaging of functionals of the calculus of variations and elasticity theory. Math USSR Izv, 1987, 9: 33–66

[2] Wang X J, Yuan R. Existence of periodic solutions for p(t)-Laplacian systems. Nonlinear Anal, 2009, 70: 866–880

[3] Dai G W, Liu W L. Three solutions for a differential inclusion problem involving the p(x)-Laplacian.Nonlinear Anal, 2009, 71: 5318–5326

[4] Ge B, Xue X P. Multiple solutions for inequality Dirichlet problems by the p(x)-Laplacian. Nonlinear Anal RWA, 2010, 11: 3198–3210

[5] Qian C Y, Shen Z F. Three solutions for a differential inclusion problem involving the p(x)-Laplacian.Nonlinear Anal RWA, 2010, 11: 106–116

[6] Dai GW. Infinitely many solutions for a hemivariational inequality involving the p(x)-Laplacian. Nonlinear Anal, 2009, 71: 186–195

[7] Dai G W. Three solutions for a Neumann-type differential inclusion problem involving the p(x)-Laplacian. Nonlinear Anal, 2009, 70: 3755–3760

[8] Dai G W. Infinitely many solutions for a Neumann-type differential inclusion problem involving the p(x)-Laplacian. Nonlinear Anal, 2009, 70: 2297–2305

[9] Filippakis M, Gasi´nski L, Papageorgiou N S. Periodic problems with asymmetric nonlinearities and nons-mooth potentials. Nonlinear Anal, 2004, 58: 683–702

[10] Denkowski Z, Gasi´nski L, Papageorgiou N S. Existence of positive and of multiple solutions for nonlinear periodic problems. Nonlinear Anal, 2007, 66: 2289–2314

[11] Aizicovici S, Papageorgiou N S, Staicu V. Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian. J Differ Equ, 2007, 243: 504–535

[12] Chang K C. Variational methods for nondifferential functionals and their applications to parial differential equations. J Math Anal Appl, 1981, 80: 102–129

[13] Gasi´nski L, Papageorgiou N S. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems. Boca Raton, FL: Chapman and Hall/CRC Press, 2005

[14] Denkowski Z, Migorski S, Papageorgiou N S. An Introduction to Nonlinear Analysis: Theory. New York: Kluwer/Plenum, 2003

[15] Motreanu D, R?adulescu V D. Variational and Non-Variational Methods in Nonlinear Analysis and Bound-ary Value Problems. Nonconvex Optimization and its Applications, Vol 67. Dordrecht: Kluwer, 2003

[16] Clarke F H. Optimization and Nonsmooth Analysis. New York: Wiley, 1993

[17] Fan X L, Fan X. A Knobloch-type result for p(t)-Laplacian systems. J Math Anal Appl, 2003, 282: 453–464

[18] Fan X L, Zhao D. On the space Lp(z)(Ω) and Wm, p(z)(Ω). J Math Anal Appl, 2001, 263: 424–446

[19] Fan X L, Zhang Q H. Existence of solutions for p(x)-Laplacian Dirichlet problems. Nonlinear Anal, 2003, 52: 1843–1852

[20] Fan X L, Zhao Y Z, Zhao D. Nodal solutions of p(x)-Laplacian equations. Nonlinear Anal, 2007, 67: 2859–2868

[21] Mawhin J, Willem M. Critical Point Theory and Hamiltonian Systems. Appl Math Sci, Vol 74. New York: Springer, 1980

[22] Papageorgiou E H, Papageorgiou N S. Existence of solutions and of multiple solutions. J Czechoslovak Mathematical, 2004, 54: 347–371

[23] Kandilakis D, Kourogenis N C, Papageorgiou N S. Two nontrivial critical points for nonsmooth functionals via local linking and applications. J Glob Optim, 2006, 34: 219–244

[24] Hu S H, Papageorgiou N S. Solutions and Multiple solutions for problem with p-Laplacian. Monatsh Math, 2007, 150: 309–326

[25] Denkowski Z, Gasinski L, Papageorgiou N S. Multiple solutions for nonautonomous second order periodic systems. Acta Math Sci, 2010, 30B(1): 350–358

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