Existence of a solution to a nonlocal Schrödinger system problem in fractional modular spaces

Adams, R.A., Fournier, J.F.: Sobolev Spaces, Second Edition, Pure and Applied Mathematics. Elsevier/Academic Press, Amsterdam (2003)

Alberico, A., Cianchi, A., Pick, L., Slavíková, L.: Fractional Orlicz-Sobolev embeddings. J. Math. Pures Appl. 149, 216–253 (2021)

Ali, K.B., et al.: On a nonlocal fractional p (.,.)-Laplacian problem with competing nonlinearities. Complex Anal. Oper. Theory 13(3), 1377–1399 (2019)

Azroul, E., Benkirane, A., Srati, M.: Nonlocal eigenvalue type problem in fractional Orlicz-Sobolev space: Nonlocal eigenvalue type problem. Adv. Oper. Theory 5, 1599–1617 (2020)

Bahrouni, A., Bahrouni, S., Xiang, M.: On a class of nonvariational problems in fractional Orlicz-Sobolev spaces. Nonlinear Anal. 190, 111595 (2020)

Bahrouni, S., Ounaies, H., Tavares, L.S.: Basic results of fractional Orlicz-Sobolev space and applications to non-local problems. Topol. Methods Nonlinear Anal. 55(2), 681–695 (2020)

Bahrouni, S., Ounaies, H.: Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems. Discrete Contin. Dyn. Syst. 40(5), 2917–2944 (2020)

Bartolo, P., Benci, V., Fortunato, D.: Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity. Nonlinear Anal. Theory Methods Appl. 7(9), 981–1012 (1983)

Bonder, J.F., Salort, A.M.: Fractional order Orlicz-Sobolev spaces. J. Funct. Anal. 277(2), 333–367 (2019)

Boumazourh, A., Srati, M.: Leray-Schauder’s solution for a nonlocal problem in a fractional Orlicz-Sobolev space. Moroccan J. Pure Appl. Anal. (MJPAA) 10, 42–52 (2020)

Brezis, H.: Analyse Fonctionnelle: Théorie et Applications. Masson, Paris (1992)

Caffarelli, L., Roquejoffre, J.M., Sire, Y.: Variational problems for free boundaries for the fractional Laplacian. J. Eur. Math. Soc. 12(5), 1151–1179 (2010)

Caffarelli, L.A., Salsa, S., Silvestre, L.: Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Invent. Math. 171(2), 425–461 (2008)

Caffarelli, L., Silvestre, L.: An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equ. 32(8), 1245–1260 (2007)

EL-Houari, H., Chadli, L.S., Hicham, M.: Existence of solution to M-Kirchhoff system type. In: 2021 7th International Conference on Optimization and Applications (ICOA), IEEE, pp. 1–6 (2021)

Fukagai, N., Ito, M., Narukawa, K.: Positive solutions of quasilinear elliptic equations with critical Orlicz–Sobolev nonlinearity on RN. Funkc. Ekvacioj 49, 235–267 (2006)

Kourogenis, N.C., Papageorgiou, N.S.: Nonsmooth critical point theory and nonlinear elliptic equations at resonance. J. Aust. Math. Soc. 69(2), 245–271 (2000)

Krasnosel’skii, M.A., Rutickii, Y.B.: Convex Functions and Orlicz Spaces, vol. 9. Noordhoff, Groningen (1961)

Kufner, A., John, O., Fucik, S.: Function Spaces. Noordhoff, Leyden (2013)

Lamperti, J.: On the isometries of certain function-spaces. Pac. J. Math. 8, 459–466 (1958)

Maia, L.A., Montefusco, E., Pellacci, B.: Positive solutions for a weakly coupled nonlinear Schrödinger system. J. Differ. Equ. 229(2), 743–767 (2006)

Menyuk, C.R.: Nonlinear pulse propagation in birefringent optical fibers. IEEE J. Quant. Electron. 23, 174–176 (1987)

Rabinowitz, P.H.: Minimax methods in critical point theory with applications to differential equations. In: Regional Conference Series in Mathematics 65. American Mathematical Society, Providence, RI (1986)

Severo, U., da Silva, E.: On the existence of standing wave solutions for a class of quasilinear Schrödinger systems. J. Math. Anal. Appl. 412(2), 763–775 (2014)

Xiang, M., Zhang, B., Wei, Z.: Existence of solutions to a class of quasilinear Schrödinger systems involving the Fractional p-Laplacian. Electron. J. Qual. Theory Differ. Equ. 107, 1–15 (2016)