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Existence of solutions for a nonlinear discrete system involving the p-Laplacian

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Abstract

The existence of solutions for boundary value problems for a nonlinear discrete system involving the p-Laplacian is investigated. The approach is based on critical point theory.

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References

  1. D. Bai, Y. Xu: Nontrivial solutions of boundary value problems of second-order difference equations. J. Math. Anal. Appl. 326 (2007), 297–302.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Bonanno, P. Candito: Nonlinear difference equations investigated via critical points methods. Nonlinear Anal., Theory Methods Appl. 70 (2009), 3180–3186.

    Article  MathSciNet  MATH  Google Scholar 

  3. G. Bonanno, P. Candito: Infinitely many solutions for a class of discrete non-linear boundary value problems. Appl. Anal. 88 (2009), 605–616.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Candito, N. Giovannelli: Multiple solutions for a discrete boundary value problem involving the p-Laplacian. Comput. Math. Appl. 56 (2008), 959–964.

    Article  MathSciNet  MATH  Google Scholar 

  5. Z.M. Guo, J. S. Yu: Existence of periodic and subharmonic solutions for second-order superlinear difference equations. Sci. China Ser. A 46 (2003), 506–515.

    MathSciNet  MATH  Google Scholar 

  6. Z.M. Guo, J. S. Yu: The existence of periodic and subharmonic solutions to subquadratic second order difference equations. J. Lond. Math. Soc., II. Ser. 68 (2003), 419–430.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Kuang: Applied Inequalities. Shandong Science and Technology Press, Jinan City, 2004. (In Chinese.)

    Google Scholar 

  8. W.D. Lu: Variational Methods in Differential Equations. Scientific Publishing House in China, 2002.

  9. J. Ma, C. L. Tang: Periodic solutions for some nonautonomous second order systems. J. Math. Anal. Appl. 275 (2002), 482–494.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Mawhin, M. Willem: Critical Point Theory and Hamiltonian Systems. Springer-Verlag, New York, 1989.

    MATH  Google Scholar 

  11. P.H. Rabinowitz: Minimax Methods in Critical Point Theory with Application to Differential Equations. Reg. Conf. Ser. Math, 65. Am. Math. Soc., Provindence, 1986.

  12. C.-L. Tang, X.-P. Wu: Notes on periodic solutions of subquadratic second order systems. J. Math. Anal. Appl. 285 (2003), 8–16.

    Article  MathSciNet  MATH  Google Scholar 

  13. J.F. Wu, X.P. Wu: Existence of nontrivial periodic solutions for a class of superquadratic second-order Hamiltonian systems. J. Southwest Univ. (Natural Science Edition) 30 (2008), 26–31.

    Google Scholar 

  14. X.-P. Wu, C.-L. Tang: Periodic solution of a class of non-autonomous second order systems. J. Math. Anal. Appl. 236 (1999), 227–235.

    Article  MathSciNet  MATH  Google Scholar 

  15. Y.-F. Xue, C.-L. Tang: Multiple periodic solutions for superquadratic second-order discrete Hamiltonian systems. Appl. Math. Comput. 196 (2008), 494–500.

    Article  MathSciNet  MATH  Google Scholar 

  16. Y.-F. Xue, C.-L. Tang: Existence of a periodic solution for subquadratic second-order discrete Hamiltonian system. Nonlinear Anal., Theory Methods Appl. 67 (2007), 2072–2080.

    Article  MathSciNet  MATH  Google Scholar 

  17. X. Zhang, X. Tang: Existence of nontrivial solutions for boundary value problems of second-order discrete systems. Math. Slovaca 61 (2011), 769–778.

    Article  MathSciNet  MATH  Google Scholar 

  18. F. Zhao, X. Wu: Periodic solutions for a class of nonautonomous second order systems. J. Math. Anal. Appl. 296 (2004), 422–434.

    Article  MathSciNet  MATH  Google Scholar 

  19. Z. Zhou, J.-S. Yu, Z.-M. Guo: Periodic solutions of higher-dimensional discrete systems. Proc. R. Soc. Edinb., Sect. A, Math. 134 (2004), 1013–1022.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Xingyong Zhang.

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This work is supported by the Graduate degree thesis Innovation Foundation of Central South University (No. 3960-71131100014) and the Outstanding Doctor degree thesis Implantation Foundation of Central South University (No. 2008yb032) and partially supported by the NNSF (No. 10771215) of China.

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Zhang, X., Tang, X. Existence of solutions for a nonlinear discrete system involving the p-Laplacian. Appl Math 57, 11–30 (2012). https://doi.org/10.1007/s10492-012-0002-2

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