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On Local and Nonlocal Discrete p-Laplacian Equations via Clark’s Theorem

  • Robert Steglinski [1]
    1. [1] Lodz University of Technology

      Lodz University of Technology

      Łódź, Polonia

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
  • Idioma: inglés
  • Enlaces
  • Resumen
    • By employing Clark’s theorem we prove the existence of infinitely many homoclinic solutions to the local and nonlocal discrete p-Laplacian equations on the integers.

      Our results extend and correct the reasoning of some recent findings expressed in the literature.

  • Referencias bibliográficas
    • 1. Balanov, Z., Garcia-Azpeitia, C., Krawcewicz, W.: On variational and topological methods in nonlinear difference equations. Commun. Pure....
    • 2. Bartsch, T., Wang, Z.Q.: Existence and multiplicity results for some superlinear elliptic problems on RN . Comm. Partial Differ. Equ. 20(910),...
    • 3. Benci, V., Fortunato, D.: Discreteness conditions of the spectrum of Schrödinger operators. J. Math. Anal. Appl. 64, 695–700 (1978)
    • 4. Ciaurri, O., Roncal, L., Stinga, P.R., Torrea, J.L., Varona, J.L.: Nonlocal discrete diffusion equations and the fractional discrete Laplacian,...
    • 5. Gasi ´nski, L., Papageorgiou, N.: Exercises in analysis. Part 1. Problem Books in Mathematics. Springer, Cham, x+1037 pp (2014)
    • 6. Graef, J.R., Kong, L., Wang, M.: Existence of homoclinic solutions for second order difference equations with p-Laplacian. Dyn. Syst. Differ....
    • 7. Iannizzotto, A., R˘adulescu, V.: Positive homoclinic solutions for the discrete p-Laplacian with a coercive weight function. Differ. Integral...
    • 8. Iannizzotto, A., Tersian, S.: Multiple homoclinic solutions for the discrete p-Laplacian via critical point theory. J. Math. Anal. Appl....
    • 9. Ju, X., Die, H., Xiang, M.: The nehari manifold method for discrete fractional p-Laplacian equations. Adv. Differ. Equ. 559, 1–21 (2020)
    • 10. Ju, C., Zhang, B.: On fractional discrete p-Laplacian equations via Clark’s theorem. Appl. Math. Comput. 434, 127443 (2022)
    • 11. Kim, J.-M., Yang, S.-O.: Multiple homoclinic orbits for a class of the discrete p-Laplacian with unbounded potentials. Math. Methods Appl....
    • 12. Kong, L.: Homoclinic solutions for a second order difference equation with p-Laplacian. Appl. Math. Comput. 247, 1113–21 (2014)
    • 13. Landkof, N.S.: Foundations of Modern Potential Theory (Translated from the Russian by A.P. Doohovskoy), Die Grundlehren der mathematischen...
    • 14. Liu, Z., Wang, Z.Q.: On clark’s theorem and its applications to partially sublinear problems. Ann. Inst. H. Poincaré Anal. Non Linéaire...
    • 15. Molica Bisci, G., Radulescu, V., Servadei, R.: Variational methods for nonlocal fractional problems, vol. 162, p. xvi+383. Cambridge...
    • 16. Motreanu, D.,Motreanu, V.V., Papageorgiou, N.: Topological and variational methods with applications to nonlinear boundary value problems,...
    • 17. Nastasi, A., Tersian, S., Vetro, C.: Homoclinic solutions of nonlinear laplacian difference equations without ambrosetti-rabinowitz condition....
    • 18. Pankov, A.: Gap solitons in periodic discrete nonlinear Schrö dinger equations. Nonlinearity 19, 27–40 (2006)
    • 19. Rabinowitz, P.H.: On a class of nonlinear Schrödinger equations. Z. Angew.Math. Phys. 43(2), 270–291 (1992)
    • 20. Salvatore, A.:Multiple solutions for perturbed elliptic equations in unbounded domains. Adv. Nonlinear Stud. 3(1), 1–23 (2003)
    • 21. Stegli ´nski, R.: On sequences of large homoclinic solutions for a difference equations on the integers. Adv. Differ. Equ. 38, 11 (2016)
    • 22. Stegli ´nski, R.: On sequences of large homoclinic solutions for a difference equations on the integers involving oscillatory nonlinearities....
    • 23. Stegli ´nski, R.: On homoclinic solutions for a second order difference equation with p-Laplacian. Discrete Contin. Dyn. Syst. Ser. B...
    • 24. Stegli ´nski, R.: Infinitely many solutions for double phase problem with unbounded potential in RN . Nonlinear Anal. 214(112580), 20...
    • 25. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton Univ. Press, Princeton, NY (1970)
    • 26. Sun, G., Mai, A.: Infinitely many homoclinic solutions for second order nonlinear difference equations with p-Laplacian. Sci. World J....
    • 27. Wu, Y., Tahar, B., Rafik, G., Rahmoune, A., Yang, L.: The existence and multiplicity of homoclinic solutions for a fractional discrete...
    • 28. Xiang, M., Zhang, B.: Homoclinic solutions for fractional discrete Laplacian equations. Nonlinear Anal. 198, 111886 (2020)

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