Infinitely many solutions for quasilinear Schrödinger equations with sign-changing nonlinearity without the aid of 4-superlinear at infinity

• Autorzy: Khiddi Mustapha , Essafi Lakbir

Identyfikatory

DOI

10.1515/dema-2022-0169

• Języki publikacji: EN

Abstrakty

EN

In this article, we will prove the existence of infinitely many solutions for a class of quasilinear Schrödinger equations without assuming the 4-superlinear at infinity on the nonlinearity. We achieve our goal by using the Fountain theorem.

Słowa kluczowe

EN

quasilinear Schrödinger; Fountain theorem; Cerami condition

PL

równanie Schrödingera; nieskończoność

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 831--842
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Khiddi Mustapha

• Département de Mathématique et Informatique, Laboratoire de Modélisation et Combinatoire, Université Cadi Ayyad, B.P. 4162 Safi, Morocco

autor

Essafi Lakbir

• Département de Mathématique et Informatique, Laboratoire de Modélisation et Combinatoire, Université Cadi Ayyad, B.P. 4162 Safi, Morocco

Bibliografia

• [1] S. Kurihara, Large-amplitude quasi-solitons in superfluid films, J. Phys. Soc. Japan 50 (1981), no. 10, 3262–3267
• [2] E. W. Laedke, K. H. Spatschek, and L. Stenflo, Evolution theorem for a class of perturbed envelope soliton solutions, J. Math. Phys. 24 (1983), no. 12, 2764–2769.
• [3] A. Nakamura, Damping and modification of exciton solitary waves, J. Phys. Soc. Japan 42 (1977), no. 6, 1824–1835.
• [4] M. Colin and L. Jeanjean, Solutions for a quasilinear Schrödinger equation: a dual approach, Nonlinear Anal. Theory Meth. Appl. 56 (2004), no. 2, 213–226.
• [5] X.-Q. Liu, J.-Q. Liu, and Z.-Q. Wang, Quasilinear elliptic equations via perturbation method, Proc. Am. Math. Soc. 141 (2013), no. 1, 253–263.
• [6] K. Wu, Positive solutions of quasilinear Schrödinger equations with critical growth, Applied Math. Lett. 45 (2015), 52–57.
• [7] X. Yang, X. Tang, and Y. Zhang, Positive, negative and sign-changing solutions to a quasilinear Schrödinger equation with a parameter, J. Math. Phys. 60 (2019), no. 12, 121510.
• [8] J. Zhang, X. Tang, and W. Zhang, Infinitely many solutions of quasilinear Schrödinger equation with sign-changing potential, J. Math. Anal. Appl. 420 (2014), no. 2, 1762–1775.
• [9] C. O. Alves, Y. Wang, and Y. Shen, Soliton solutions for a class of quasilinear Schrödinger equations with a parameter, J. Differential Equations 259 (2015), no. 1, 318–343.
• [10] C. O. Alves and G. M. Figueiredo, Multiple solutions for a quasilinear Schrödinger equation on RN, Acta Applicandae Mathematicae 136 (2015), no. 1, 91–117.
• [11] C. O. Alves, G. M. Figueiredo, and U. B. Severo, A result of multiplicity of solutions for a class of quasilinear equations, Edinburgh Math. Soc. Proc. Edinburgh Math. Soc. 55 (2012), no. 2, 291.
• [12] M. Willem, Minimax Theorems, Progress in nonlinear differential equations and their applications, vol. 24, Birkhäuser Boston Inc., Boston, 1996.
• [13] T. Bartsch and Z. Q. Wang, Existence and multiplicity results for some superlinear elliptic problems on RN : Existence and multiplicity results, Comm. Partial Differential Equations 20 (1995), no. 9–10, 1725–1741.
• [14] T. Bartsch, Z.-Q. Wang, and M. Willem, The Dirichlet problem for superlinear elliptic equations, Handbook Differential Equations-Stationary Partial Differential Equations 2 (2005), no. 1, 1–55.
• [15] J.-Q. Liu, Y.-Q. Wang, and Z.-Q. Wang, Soliton solutions for quasilinear Schrödinger equations, ii, J. Differential Equations 187 (2003), no. 2, 473–493.
• [16] R. Adams, Sobolev Spaces, vol. 1, AC Press, New York, 1975, p. 975.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).