Two classes of infinitely many solutions for fractional Schrödinger-Maxwell system with concave-convex power nonlinearities

• Autorzy: Khiddi Mustapha

Identyfikatory

DOI

10.7862/rf.2022.4

• Języki publikacji: EN

Abstrakty

EN

Employing critical theory and concentration estimates, we establish the existence of two classes of infinitely many weak solutions fractional Schrödinger-Poisson system involving critical Sobolev growth. The first classe of solutions with negative energy is found by using of notion genus while the second one contains infinitely many weak solutions with positive energy via Fountain theorem.

Słowa kluczowe

EN

fractional system; critical exponents; Fountain theorem; genus; concentration-compactness

PL

układ ułamkowy; wykładnik krytyczny; rodzaj

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2022
• Tom: Vol. 45
• Strony: 87--105
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Khiddi Mustapha

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

• https://orcid.org/0000-0001-5749-5807

Bibliografia

• [1] R. Adams, Sobolev Spaces, Ac. Press, New York, 1975.
• [2] A. Ambrosetti, D. Ruiz, Multiple bound states for the Schrödinger-Poisson problem, Communications in Contemporary Mathematics 10 (03) (2008) 391-404.
• [3] V. Benci, D. F. Fortunato, Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equations, Reviews in Mathematical Physics 14 (04) (2002) 409-420.
• [4] H. Brézis, E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proceedings of the American Mathematical Society 88 (3) (1983) 486-490.
• [5] I. Catto, P.L. Lions, A necessary and sufficient condition for the stability of general molecular systems, Communications in Partial Differential Equations 17 (7-8) (1992) 1051-1110.
• [6] T. D’Aprile, D. Mugnai, Non-existence results for the coupled Klein-Gordon-Maxwell equations, Advanced Nonlinear Studies 4 (3) (2004) 307-322.
• [7] E. Di Nezza, G. Palatucci, E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bulletin des Sciences Mathématiques 136 (5) (2012) 521-573.
• [8] X. He, W. Zou, Existence and concentration of ground states for Schrödinger-Poisson equations with critical growth, Journal of Mathematical Physics 53 (2) (2012) 023702.
• [9] O. Kavian, Introduction à la théorie des points critiques et applications aux problèmes elliptiques, Springer-Verlag, France, Paris, 1993.
• [10] M. Khiddi, S.M. Sbai, Infinitely many solutions for non-local elliptic non-degenerate p-Kirchhoff equations with critical exponent, Complex Variables and Elliptic Equations (2019) pages 1-13.
• [11] M. Khiddi, S.M. Sbai, Infinitely many solutions for non-local elliptic non-degenerate p-Kirchhoff equations with critical exponent, Complex Variables and Elliptic Equations 65 (3) (2020) 368-380.
• [12] M. Khiddi, Multiple solutions for the fractional Schrödinger-Poisson system with critical Sobolev exponent, Rocky Mountain Journal of Mathematics 52 (2) (2022) 535-545.
• [13] W. Krawcewicz, W. Marzantowicz, Some remarks on the Lusternik-Schnirelman method for non-differentiable functionals invariant with respect to a finite group action, The Rocky Mountain Journal of Mathematics 20 (4) (1990) 1041-1049.
• [14] E.H. Lieb, B. Simon, The Thomas-Fermi theory of atoms, molecules and solids, Advances in Mathematics 23 (1) (1977) 22-116.
• [15] Z. Liu, J. Zhang, Multiplicity and concentration of positive solutions for the fractional Schrödinger-Poisson systems with critical growth, ESAIM: Control, Optimisation and Calculus of Variations 23 (4) (2017) 1515-1542.
• [16] E.G. Murcia, G. Siciliano, et al. Positive semiclassical states for a fractional Schrödinger-Poisson system, Differential and Integral Equations 30 (3/4) (2017) 231-258.
• [17] G. Palatucci, A. Pisante, Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces, Calculus of Variations and Partial Differential Equations 50 (3-4) (2014) 799-829.
• [18] G. Palatucci, A. Pisante, Y. Sire, Subcritical approximation of a Yamabe type non local equation: a gamma-convergence approach, arXiv preprint arXiv:1306.6782, 2013.
• [19] M. Struwe, Variational Methods, volume 31999, Springer, 1990.
• [20] K. Teng, Existence of ground state solutions for the nonlinear fractional Schrödinger-Poisson system with critical Sobolev exponent, Journal of Differential Equations 261 (6) (2016) 3061-3106.
• [21] J. Wang, L. Tian, J. Xu, F. Zhang, Existence of multiple positive solutions for Schrödinger-Poisson systems with critical growth, Zeitschrift für Angewandte Mathematik und Physik 66 (5) (2015) 2441-2471.
• [22] M. Willem, Minimax theorems: Progress in nonlinear differential equations and applications, 24, Birkhäuser, Boston, Basel, Berlin, 1996.