Geodesic
Existence of~a~solution to~a~nonlinear elliptic equation in a~Musielak--Orlicz--Sobolev space for~an~unbounded domain
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2055-2067.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a class of second-order elliptic equations with nonlinearities defined by generalized $N$-functions. The existence of a weak solution to the Dirichlet problem in a reflexive Musielak–Orlicz–Sobolev space is proved for an arbitrary unbounded domain.
Keywords: Musielak–Orlicz-Sobolev space, Dirichlet problem, pseudomonotone operator, unbounded domain.
Mots-clés : $\Delta_2$-condition, existence of a solution 
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     title = {Existence of~a~solution to~a~nonlinear elliptic equation in {a~Musielak--Orlicz--Sobolev} space for~an~unbounded domain},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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L. M. Kozhevnikova; A. P. Kashnikova. Existence of~a~solution to~a~nonlinear elliptic equation in a~Musielak--Orlicz--Sobolev space for~an~unbounded domain. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2055-2067. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a111/

[1] F.E. Browder, “Pseudo-monotone operators and nonlinear elliptic boundary value problems on unbounded domains”, Proc. Natl. Acad. Sci. USA, 74:7 (1977), 2659–2661 | DOI | MR | Zbl

[2] L.M. Kozhevnikova, A. Sh. Kamaletdinov, “Existence of solutions of anisotropic elliptic equations with variable nonlinearity exponents in unbounded domains”, Vestn. Volgogr. Gos. Univ. Ser. 1. Mat. Fiz., 5:36 (2016), 29–41 | DOI | MR

[3] L.M. Kozhevnikova, A.A. Khadzhi, “Existence of solutions of anisotropic elliptic equations with nonpolynomial nonlinearities in unbounded domains”, Sb. Math., 206:8 (2015), 1123–1149 | DOI | MR | Zbl

[4] M. Mihăilescu, V. Rădulescu, “Neumann problems associated to nonhomogeneous differential operators in Orlicz-Sobolev spaces”, Ann. Inst. Fourier, 58:6 (2008), 2087–2111 | DOI | MR | Zbl

[5] X. Fan, C.-X. Guan, “Uniform convexity of Musielak-Orlicz-Sobolev spaces and applications”, Nonlinear Anal., 73:1 (2010), 163–175 | DOI | MR | Zbl

[6] A. Benkirane, M. Sidi El Vally, “An existence result for nonlinear elliptic equations in Musielak-Orlicz-Sobolev spaces”, Bull. Belg. Math. Soc.-Simon Stevin, 20:1 (2013), 57–75 | DOI | MR | Zbl

[7] M. Sidi El Vally, “Strongly Nonlinear Elliptic Problems in Musielak-Orlicz-Sobolev Spaces”, Advances in Dynamical Systems and Applications, 8:1 (2013), 115–124 | MR

[8] G. Dong, X. Fang, “Differential equations of divergence form in separable Musielak-Orlicz-Sobolev spaces”, Boundary Value Problems, 2016:106 (2016), 1–19 | DOI | MR

[9] L. Diening, P. Harjulehto, P. Hästö, M. Ru{z}i{c}ka, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, 2017, Springer, Berlin, 2011 | DOI | MR | Zbl

[10] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, 1034, Springer-Verlag, Berlin etc., 1983 | DOI | MR | Zbl

[11] M.A. Krasnosel'skii, Ja. B. Rutickii, Convex functions and Orlicz spaces, P. Noordhoff Ltd., Groningen, 1961 | MR | Zbl

[12] J.P. Gossez, “Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients”, Trans. Am. Math. Soc., 190 (1974), 163–206 | DOI | MR | Zbl

[13] N. Dunford, J.T. Schwartz, Linear operators, v. I, Pure Appl. Math., 7, General theory, Interscience Publishers, Inc., New York–London, 1958 | MR | Zbl

[14] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1969 | MR | Zbl