A class of elliptic inclusion in fractional Orlicz–Sobolev spaces

References

• Clarke FH. Optimization and nonsmooth analysis. Philadelphia: Society for Industrial and Applied Mathematics; 1990.
   Google Scholar
• Bonder JF, Salort AM. Fractional order Orlicz-Sobolev spaces. J Funct Anal. 2019;277(2):333–367.
   Web of Science ®Google Scholar
• Azroul E, Benkirane A, Srati M. Existence of solutions for a non-local type problem in fractional Orlicz Sobolev spaces. Adv Oper Theory. 2020;5(4):1350–1375.
   Web of Science ®Google Scholar
• Azroul, E, Benkirane, A, Boumazough, A, et al. Multiple solutions for a nonlocal fractional (p, q)-Schrodinger-Kirchhoff type system. Nonlinear Stud. 2020;27(4):915–933.
   Google Scholar
• Bahrouni S, Ounaies H, Tavares LS. Basic results of fractional Orlicz-Sobolev space and applications to non-local problems. Topol Methods Nonlinear Anal. 2020;55(2):681–695.
   Web of Science ®Google Scholar
• Bahrouni A, Bahrouni S, Xiang M. On a class of nonvariational problems in fractional Orlicz–Sobolev spaces. Nonlinear Anal. 2020;190:111595.
   Web of Science ®Google Scholar
• El-Houari H, Chadli LS, Moussa H. Existence of a solution to a nonlocal Schrödinger system problem in fractional modular spaces. Adv Oper Theory. 2022;7(1):1–30.
   Web of Science ®Google Scholar
• Hamza EH, Chadli LS, Moussa H. Existence of ground state solutions of elliptic system in fractional Orlicz-Sobolev spaces. Results Nonlinear Anal. 5(2):112–130.
   Google Scholar
• Dong G, Fang X. Positive solutions to nonlinear inclusion problems in Orlicz–Sobolev spaces. Appl Anal. 2021;100(7):1440–1453.
   Web of Science ®Google Scholar
• Yuan Z, Huang L, Wang D. Existence and multiplicity of solutions for a quasilinear elliptic inclusion with a nonsmooth potential. Taiwan J Math. 2018;22(3):635–660.
   Web of Science ®Google Scholar
• Iannizzotto A, Rocha EM, Sandrina S. Two solutions for fractional p-Laplacian inclusions under nonresonance. Electron J Differ Equ 2018;122:1–14.
   Google Scholar
• Kim IH, Kim YH, Park K. On discontinuous elliptic problems involving the fractional p-Laplacian in RN. Bull Korean Math Soc. 2018;55(6):1869–1889.
   Web of Science ®Google Scholar
• Yuan Z, Huang M. Existence and multiplicity of solutions for p(x)-Laplacian differential inclusions involving critical growth. J Appl Anal Comput. 2020;10(4):1416–1432.
   Google Scholar
• Motreanu D, Varga C. Some critical point results for locally Lipschitz functionals. Comm Appl Nonlinear Anal. 1997;4:17–33.
   Google Scholar
• Ali KB, Hsini M, Kefi K, et al. On a nonlocal fractional p(⋅,⋅)-Laplacian problem with competing nonlinearities. Complex Anal Oper Theory. 2019;13(3):1377–1399.
   Web of Science ®Google Scholar
• Krasnosel'skii MA, Rutickii YB. Convex functions and Orlicz spaces. Vol. 9, Groningen: Noordhoff; 1961.
   Google Scholar
• Kufner A, John O, Fucik S. Function spaces. Leyden: Noordhoff; 2013.
   Google Scholar
• Boumazourh A, Srati M. Leray-Schauder's solution for a nonlocal problem in a fractional Orlicz-Sobolev space. Moroccan J Pure Appl Anal. 2020;6(1):42–52.
   Google Scholar
• MiricÇŐ S. A note on the generalized differentiability of mappings. Nonlinear Anal Theory Methods Appl. 1980;4(3):567–575.
   Google Scholar
• Clément P, De Pagter B, Sweers G, et al. Existence of solutions to a semilinear elliptic system through Orlicz-Sobolev spaces. Mediterr J Math. 2004;1(3):241–267.
   Google Scholar
• Fukagai N, Ito M, Narukawa K. Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on RN. Funkcial Ekvac. 2006;49(2):235–267.
   Web of Science ®Google Scholar
• Carl S, Le VK, Motreanu D. Nonsmooth variational problems and their inequalities: comparison principles and applications. New York: Springer Science & Business Media; 2007.
   Google Scholar
• Denkowski Z, Migorski S, Papageorgiou NS. An introduction to nonlinear analysis: theory. New York: Springer Science & Business Media; 2003.
   Google Scholar
• Adams RA. Sobolev spaces. New York (NY): Academic Press; 1975.
   Google Scholar