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

doi:10.1016/S0252-9602(11)60361-5

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (5): 1786-1802.doi: 10.1016/S0252-9602(11)60361-5

• Articles • Previous Articles Next Articles

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

GE Bin^*, XUE Xiao-Ping, ZHOU Qiang-Mei

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:2010-05-12 Revised:2010-09-05 Online:2011-09-20 Published:2011-09-20
Contact: GE Bin，gebin04523080261@163.com E-mail:gebin04523080261@163.com；xiaopingxue@263.net；zhouqingmei2008@163.com
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).

Abstract

CLC Number:

34C25

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.

Trendmd

[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 L^p^(z)(Ω) and W^m,^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

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

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Mohammed Salah M'HAMDI, Chaouki AOUITI, Abderrahmane TOUATI, Adel M. ALIMI, Vaclav SNASEL. WEIGHTED PSEUDO ALMOST-PERIODIC SOLUTIONS OF SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH MIXED DELAYS [J]. Acta mathematica scientia,Series B, 2016, 36(6): 1662-1682.
[2]	Chunhua JIN, Tong YANG. TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN [J]. Acta mathematica scientia,Series B, 2016, 36(4): 1015-1029.
[3]	Adnène ARBI, Farouk CHÉRIF, Chaouki AOUITI, Abderrahmen TOUATI. DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS [J]. Acta mathematica scientia,Series B, 2016, 36(3): 891-912.
[4]	Hong CAI, Zhong TAN. WEAK TIME-PERIODIC SOLUTIONS TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS [J]. Acta mathematica scientia,Series B, 2016, 36(2): 499-513.
[5]	Sahbi BOUSSANDEL. EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES [J]. Acta mathematica scientia,Series B, 2016, 36(1): 233-243.
[6]	Renjun DUAN, Shuangqian LIU. TIME-PERIODIC SOLUTIONS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM [J]. Acta mathematica scientia,Series B, 2015, 35(4): 876-886.
[7]	XU Qiu Ju,CAI Hong,TAN Zhong. TIME PERIODIC SOLUTIONS OF NON-ISENTROPIC COMPRESSIBLE MAGNETOHYDRODYNAMIC SYSTEM [J]. Acta mathematica scientia,Series B, 2015, 35(1): 216-234.
[8]	Philip KORMAN, Yi LI. HARMONIC OSCILLATORS AT RESONANCE, PERTURBED BY A NON-LINEAR FRICTION FORCE [J]. Acta mathematica scientia,Series B, 2014, 34(4): 1025-1028.
[9]	LU Shi-Ping, ZHENG Liang, CHEN Li-Juan. HOMOCLINIC SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS [J]. Acta mathematica scientia,Series B, 2013, 33(5): 1361-1374.
[10]	LIU Gui-Fang, LIU Yi-Liang. ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS [J]. Acta mathematica scientia,Series B, 2012, 32(4): 1426-1434.
[11]	Zdzislaw Denkowski, Leszek Gasinski, Nikolaos S. Papageorgiou. MULTIPLE SOLUTIONS FOR NONAUTONOMOUS SECOND ORDER PERIODIC SYSTEMS [J]. Acta mathematica scientia,Series B, 2010, 30(1): 341-349.
[12]	Blake Temple, Robin Young. LINEAR WAVES THAT EXPRESS THE SIMPLEST POSSIBLE PERIODIC STRUCTURE OF THE COMPRESSIBLE EULER EQUATIONS [J]. Acta mathematica scientia,Series B, 2009, 29(6): 1749-1766.
[13]	JIANG Xin-Hua, WANG Zhen. PERTURBED PERIODIC SOLUTION FOR BOUSSINESQ EQUATION [J]. Acta mathematica scientia,Series B, 2009, 29(3): 705-722.
[14]	Dong Lingzhen; Chen Lansun; Sun Lihua. OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION [J]. Acta mathematica scientia,Series B, 2007, 27(2): 405-412.
[15]	Fu Yiping; Guo Boling. ALMOST PERIODIC SOLUTION OF ONE DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATION [J]. Acta mathematica scientia,Series B, 2007, 27(1): 117-124.