An Elliptic Type Inclusion Problem on the Heisenberg Lie Group

REFERENCES

[1] AUBIN, J. P.—FRANKOWSKA, H.: Set-valuedAnalysis, Birkhäauser, Boston, 1990.Search in Google Scholar

[2] APPELL, A.—DE PASCALE, E.—ZABREJKO, P. P.: Multivalued superposition operators, Rend. Semin. Mat. Univ. Padova 86 (1991), 213–231. 10.1017/CBO9780511897450Search in Google Scholar

[3] AUMANN, R. J.: Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1–12. 10.1016/0022-247X(65)90049-1Search in Google Scholar

[4] BADIALE, M.—SERRA, E.: Semilinear Elliptic Equations for Beginners: Existence results via the Variational Approach, Springer, 2011. 10.1007/978-0-85729-227-8Search in Google Scholar

[5] CENCELJ, M.—RĂDULESCU,V.D.—REPOVŠ, D.: Double phase problems with variable growth, Nonlinear Anal. 177 (2018), 270–287. 10.1016/j.na.2018.03.016Search in Google Scholar

[6] CHANG, K. C: Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80(1) (1981), 102–129. 10.1016/0022-247X(81)90095-0Search in Google Scholar

[7] CLARKE, F. H.: Optimization and Nonsmooth Analysis, Wiley, New York, 1983. Search in Google Scholar

[8] COLASUONNO, F.—IANNIZZOTTO, A.—MUGNAI, D.: Three solutions for a Neumann partial differential inclusion via nonsmooth Morse theory, Set Valued Var. Anal. 25 (2017), 405–425.10.1007/s11228-016-0387-2Search in Google Scholar

[9] GAROFALO, N.—NHIEU, D. M.: Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces, Commun. Pure Appl. Math. 49(10) (1996), 1081–1144. 10.1002/(SICI)1097-0312(199610)49:10<1081::AID-CPA3>3.0.CO;2-ASearch in Google Scholar

[10] GASIŃKSI, L.—PAPAGEORGIOU, N. S.: Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, Chapman and Hall, Bokca Raton, 2005. 10.1201/9780367801632Search in Google Scholar

[11] HEIDARI, S.—RAZANI, A.: Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz-Sobolev spaces, Bound. Value Probl. 2021 (2021), Art. No. 22. 10.1186/s13661-021-01496-8Search in Google Scholar

[12] HEIDARI, S.—RAZANI, A.: Infinitely many solutions for nonlocal elliptic systems in Orlicz-Sobolev spaces, Georgian Math. J. 29(1) (2021), 45–54. 10.1515/gmj-2021-2110Search in Google Scholar

[13] IANNIZZOTTO, A.: Recent advances in nonlinear PDEs theory. Lect. Notes Semin. Interdiscip. Mat. 13, Semin. Interdiscip. Mat. (S.I.M.), Potenza, 2016, pp. 35–46.Search in Google Scholar

[14] IVANOV, S. P.—VASSILEV, D. N.: Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem, World Scientific, Publishing Co. Pte. Ltd., Hackensack, N. J., 2011. 10.1142/7647Search in Google Scholar

[15] KOTONAJ, E.Z.: Aumann integral of set value mappings valued in quasy-Banach spaces and some of its properties, Internat. J. Math. Trends Tech. 12 (2014), 63–68.10.14445/22315373/IJMTT-V12P510Search in Google Scholar

[16] MINGIONE, G.—RĂDULESCU, V.: Recent developments in problems with nonstandard growth and nonuni-form ellipticity, J. Math. Anal. Appl. 501(1) (2021), Art. ID 125197. 10.1016/j.jmaa.2021.125197Search in Google Scholar

[17] O’REGAN, D.—MEEHAN, M.: Existence theory for nonlinear integral and integrodifferential equations, Mathematics and its Application 445, Springer Science and Business Media, 2012. Search in Google Scholar

[18] PUCCI, P.—TEMPERINI, L.: Existence for (p,q)-critical systems in the Heisenberg group, Adv. Nonlinear Anal. 9(1) (2020), 895–922. 10.1515/anona-2020-0032Search in Google Scholar

[19] PEDERSEN, G. K.: The existence and uniqueness of the Haar integral on a locally compact topological group, preprint, University of Copenhagen, November 2000, 2004-2.Search in Google Scholar

[20] RAGUSA, M. A.—RAZANI, A.—SAFARI, F.: Existence of positive radial solutions for a problem involving weighted Heisenberg p(·)-Laplacian operator, AIMS Mathematics 8 (2022), 404–422. 10.3934/math.2023019Search in Google Scholar

[21] RAZANI, A.—FIGUEIREDO, G. M.: Degenerated and competing anisotropic (p,q)-Laplacians with weights, Appl. Anal. (2022). 10.1186/s13661-022-01669-zSearch in Google Scholar

[22] RAZANI, A.—FIGUEIREDO, G. M.: A positive solution for an anisotropic p,q-Laplacian, Discrete Contin. Dyn. Syst. - S 16(6) (2023), 1629–1643. 10.3934/dcdss.2022147Search in Google Scholar

[23] RAZANI, A.—FIGUEIREDO, G.M.: Existence of infinitely many solutions for an anisotropic equation using genus theory, Math. Methods Appl. Sci. (2022). 10.22541/au.164555393.37079597/v1Search in Google Scholar

[24] RAZANI, A.—FIGUEIREDO, G. M.: Weak solution by sub-supersolution method for a nonlocal elliptic system involving Lebesgue generalized spaces, Electron. J. Differ. Equ. 36 (2022), 1–18. 10.58997/ejde.2022.36Search in Google Scholar

[25] RAZANI, A.—SAFARI, F.: Existence of radial weak solutions to Steklov problem involving Leray-Lions type operator, J. Nonlinear Math. Phys. 30 (2023), 184–200. 10.1007/s44198-022-00078-1Search in Google Scholar

[26] RICCIOTTI, D.: p-Laplace Equation in the Heisenberg Group: Regularity of Solutions, Springer, 2015. 10.1007/978-3-319-23790-9Search in Google Scholar

[27] SAFARI, F.—RAZANI, A.: Existence of positive radial solutions for Neumann problem on the Heisenberg group, Bound. Value Probl. 2020 (2020), Art. No. 88. 10.1186/s13661-020-01386-5Search in Google Scholar

[28] SAFARI, F.—RAZANI, A.: Nonlinear nonhomogeneous Neumann problem on the Heisenberg group, Appl. Anal. 101(7) (2022), 2387–2400. 10.1080/00036811.2020.1807013Search in Google Scholar

[29] SAFARI, F.—RAZANI, A.: Existence of radial solutions of the Kohn-Laplacian problem, Complex Var. Elliptic Equ. 67(2) (2022), 259–273. 10.1080/17476933.2020.1818733Search in Google Scholar

[30] SAFARI, F.—RAZANI, A.: Existence of radial solutions for a weighted p-biharmonic problem with Navier boundary condition on the Heisenberg group, Math. Slovaca 72(3) (2022), 677–692. 10.1515/ms-2022-0046Search in Google Scholar

[31] SOLTANI, T.—RAZANI, A.: Solutions to some systems of nonlocal problems on a bounded domain, Iran J. Sci. Technol. Trans. A. Sci. (2022), 1-8.10.1007/s40995-022-01356-9Search in Google Scholar

[32] SHI, X.—RADULESCU, V. D.—REPOVS, D.—ZHANG, Q.: Multiple solutions of double phase variational problems with variable exponent, Adv. Calc. Var. 13(4) (2020), 385–401.10.1515/acv-2018-0003Search in Google Scholar