×

Ground state solutions for a nonlocal system in fractional Orlicz-Sobolev spaces. (English) Zbl 1501.35180


MSC:

35J50 Variational methods for elliptic systems
35R11 Fractional partial differential equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A15 Variational methods applied to PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Fernández Bonder, J.; Salort, A. M., Fractional order orlicz-sobolev spaces, Journal of Functional Analysis, 277, 2, 333-367 (2019) · Zbl 1426.46018 · doi:10.1016/j.jfa.2019.04.003
[2] Azroul, E.; Boumazourh, A., On a class of fractional systems with nonstandard growth conditions, J. PseudoDiffer. Oper. Appl., 11, 805-820 (2020) · Zbl 1440.35150
[3] Adriouch, K.; El Hamidi, A., The Nehari manifold for systems of nonlinear elliptic equations, Nonlinear Analysis: Theory, Methods & Applications, 64, 10, 2149-2167 (2006) · Zbl 1194.35132 · doi:10.1016/j.na.2005.06.003
[4] Afrouzi, G. A.; Heidarkhani, S., Existence of three solutions for a class of Dirichlet quasilinear elliptic systems involving the (p1,…,pn) -Laplacian, Nonlinear Analysis: Theory, Methods & Applications, 70, 1, 135-143 (2009) · Zbl 1161.35371 · doi:10.1016/j.na.2007.11.038
[5] Boccardo, L.; Guedes de Figueiredo, D., Some remarks on a system of quasilinear elliptic equations, NoDEA : Nonlinear Differential Equations and Applications, 9, 3, 309-323 (2002) · Zbl 1011.35050 · doi:10.1007/s00030-002-8130-0
[6] El-Houari, H.; Chadli, L. S.; Moussa, H., Existence of a solution to a nonlocal Schrödinger system problem in fractional modular spaces, Advances in Operator Theory, 7, 1, 1-30 (2022) · Zbl 1481.35206 · doi:10.1007/s43036-021-00166-x
[7] Halsey, T. C., Electrorheological fluids, Science, 258, 5083, 761-766 (1992) · doi:10.1126/science.258.5083.761
[8] Diening, L., Theorical and Numerical Results for Electrorheological Fluids (2002), Germany: University of Freiburg, Germany, Ph.D. thesis · Zbl 1022.76001
[9] Chen, Y.; Levine, S.; Rao, M., Variable exponent, linear growth functionals in image restoration, SIAM Journal on Applied Mathematics, 66, 4, 1383-1406 (2006) · Zbl 1102.49010 · doi:10.1137/050624522
[10] Azroul, E.; Benkirane, A.; Srati, M.; Shimi, M., Existence of solutions for a nonlocal Kirchhoff type problem in Fractional Orlicz-Sobolev spaces (2019), https://arxiv.org/abs/1901.05216
[11] Bahrouni, A.; Bahrouni, S.; Xiang, M., On a class of nonvariational problems in fractional Orlicz-Sobolev spaces, Nonlinear Analysis, 190, 111595 (2020) · Zbl 1430.35084 · doi:10.1016/j.na.2019.111595
[12] El-houari, H.; Chadli, L. S.; Moussa, M., Existence of solution to M-Kirchhoff system type, 2021 7th International Conference on Optimization and Applications (ICOA) (2021), IEEE · doi:10.1109/icoa51614.2021.9442669
[13] Corrêa, F. J. S. A.; Carvalho, M. L. M.; Goncalves, J. V. A.; Silva, K. O., Positive solutions of strongly nonlinear elliptic problems, Asymptotic Analysis, 93, 1-2, 1-20 (2015) · Zbl 1332.35249 · doi:10.3233/asy-141278
[14] Adams, R. A.; Fournier, J. F., Sobolev Spaces Pure and Applied Mathematics (2003), Amsterdam: Elsevier/Academic Press, Amsterdam · Zbl 1098.46001
[15] Ali, K. B.; Hsini, M.; Kefi, K.; Chung, N. T., On a nonlocal fractional p(., .)-Laplacian problem with competing nonlinearities, Complex Analysis and Operator Theory, 13, 3, 1377-1399 (2019) · Zbl 1419.35197 · doi:10.1007/s11785-018-00885-9
[16] Bahrouni, S.; Ounaies, H.; Tavares, L. S., Basic results of fractional Orlicz-Sobolev space and applications to non-local problems, Topological Methods in Nonlinear Analysis, 55, 2, 681-695 (2020) · Zbl 1448.35242 · doi:10.12775/tmna.2019.111
[17] Krasnosel’skii, M. A.; Rutickii, Y. B., Convex Functions and Orlicz Spaces, 9 (1961), Groningen: Noordhoff, Groningen · Zbl 0095.09103
[18] Fukagai, N.; Ito, M.; Narukawa, K., Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on RN, Funkcialaj Ekvacioj, 49, 2, 235-267 (2006) · Zbl 1387.35405 · doi:10.1619/fesi.49.235
[19] Azroul, E.; Benkirane, A.; Srati, M., Existence of solutions for a nonlocal type problem in fractional Orlicz Sobolev spaces, Advances in Operator Theory, 5, 4, 1350-1375 (2020) · Zbl 1445.35296 · doi:10.1007/s43036-020-00042-0
[20] Wang, L.; Zhang, X.; Fang, H., Existence and multiplicity of solutions for a class of (ϕ1, ϕ2)-Laplacian elliptic system in RN via genus theory (ɸ_1ɸ_2)-Laplacian elliptic system in R^Nvia genus theory, Computers & Mathematics with Applications, 72, 1, 110-130 (2016) · Zbl 1443.35035 · doi:10.1016/j.camwa.2016.04.034
[21] Boumazourh, A.; Srati, M., Leray-Schauder’s solution for a nonlocal problem in a fractional Orlicz-Sobolev space, Moroccan Journal of Pure and Applied Analysis, 6, 1, 42-52 (2020) · doi:10.2478/mjpaa-2020-0004
[22] Corrêa, F. J. S. A.; Carvalho, M. L. M.; Goncalves, J. V. A.; Silva, E. D., Sign changing solutions for quasilinear superlinear elliptic problems, The Quarterly Journal of Mathematics, 68, 2, 391-420 (2017) · Zbl 1377.35115 · doi:10.1093/qmath/haw047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.