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On the existence of a solution for a strongly nonlinear elliptic perturbed anisotropic problem of infinite order with variable exponents | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 5، دوره 16، شماره 3، خرداد 2025، صفحه 53-62 اصل مقاله (365.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.32715.4870 | ||
| نویسنده | ||
| Hakima Ouyahya* | ||
| Equipe EDP et Calcul Scientifique, Laboratoire de Mathematiques et Leurs Interactions, Faculte des Sciences, Moulay Ismail University, Meknes, Morocco | ||
| تاریخ دریافت: 29 آذر 1402، تاریخ بازنگری: 27 دی 1402، تاریخ پذیرش: 29 دی 1402 | ||
| چکیده | ||
| In this work, we shall be interested in the existence of a solution to the following Dirichlet problem for a specific class of elliptical anisotropic equations of the type \begin{eqnarray}\label{P.1} \left \{\begin{array}{rl} &A(u)+g(x,u)= f \ \ {\rm in}\ \Omega %[1.5ex] \\ %[1ex] & u=0\ \ {\rm on}\ {\partial \Omega}, \end{array} \right. \end{eqnarray} where $\Omega$ is a bounded open set of $\mathbb{R}^{N},$ $A=\sum_{|\alpha|=0}^{\infty}(-1)^{|\alpha|}D^{\alpha}\big(a_{\alpha}|D^{\alpha}u|^{p_{\alpha}(x)-2}D^{\alpha}u\big)$ is an operator of infinite order and $g(x, s )$ is a non-linear lower order term that verify some natural growth and sign conditions, where the data $f$ is framed in $L^1(\Omega)$. | ||
| کلیدواژهها | ||
| Strongly nonlinear elliptic equations of infinite order؛ monotonicity condition؛ variable exponents؛ sign condition | ||
| مراجع | ||
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[1] M.H. Abdou, A. Benkirane M. Chrif, and S. El Manouni, Strongly anisotropic elliptic problems of infinite order with variable exponents, Complex Var. Elliptic Equ. 59 (2014), no. 10, 1403–1417. [2] E. Acerbi and G. Mingione, Gradient estimates for the p(x)-Laplacian system, J. Reine Angew. Math. 584 (2005), 117–148. [3] R. Adams, Sobolev Spaces, Press New York, 1975. [4] C.O. Alves and M.A. Souto, Existence of solutions for a class of problems in IRN involving the p(x)-Laplacian, T. Cazenave, D. Costa, O. Lopes, R. Manasevich, P. Rabinowitz, B. Ruf, C. Tomei (Eds.), Contributions to Nonlinear Analysis, A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday, Progr. Nonlinear Differential Equations Appl., vol. 66, Birkh¨auser, Basel, 2006, pp. 17–32. [5] A. Benkirane M. Chrif, and S. El Manouni, Existence results for strongly nonlinear equations of infinite order, Z. Anal. Anwend. (J. Anal. Appl.) 26 (2007), 303–312. [6] H. Brezis, Analyse fonctionelle: Theorie, Methodes et Applications, Masson, Paris, 1992. [7] J. Chabrowski and Y. Fu, Existence of solutions for p(x)-Laplacian problems on a bounded domain, J. Math. Anal. Appl. 306 (2005), 604–618. [8] M. Chrif and S. El Manouni, On a strongly anisotropic equation with L1-data, Appl. Anal. 87 (2088), no. 7, 865–871. [9] M. Chrif and S. El Manouni, Anisotropic equations in weighted Sobolev spaces of higher order, Ricerche Mat. 58 (2009), 1–14. [10] L. Diening, Theoretical and numerical results for electrorheological fluids, PhD thesis, University of Freiburg, Germany, 2002. [11] L. Diening, P. Harjulehto, P. Hasto, and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, vol. 2017, Springer-Verlag, Berlin, 2011. [12] J.A. Dubinskii, Sobolev spaces for infinite order and the behavior of solutions of some boundary value problems with unbounded increase of the order of the equation, Math. USSR-Sb. 27 (1975), no. 2, 143–162. [13] J.A. Dubinskii, Sobolev Spaces of Infinite Order and Differential Equations, Teubner-Texte Math., Band 87. Leipzig: Teubner, 1986. [14] D.E. Edmunds, J. Lang, and A. Nekvinda, On Lp(x) norms, Proc. Roy. Soc. London Ser. A 455 (1999), 219–225. [15] D.E. Edmunds and J. Rakosnik, Density of smooth functions in Wk,p(x)(Ω), Proc. Roy. Soc. London Ser. A 437 (1992), 229–236. [16] D.E. Edmunds and J. Rakosnık, Sobolev embedding with variable exponent, Studia Math. 143 (2000), 267–293. [17] X.L. Fan, D. Zhao, On the generalized Orlicz-Sobolev space Wk,p(x)(Ω), J. Gansu Educ. College 12 (1998), no. 1, 1–6. [18] P. Harjulehto, P. Hasto, U. V. Le, and M. Nuortio, Overview of differential equations with non-standard growth, Nonlinear Anal. 72 (2010), 4551–4574. [19] T.C. Halsey, Electrorheological fluids, Science 258 (1992), 761–766. [20] S. Heidari and A. Razani, Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz-Sobolev spaces, Bound. Value Prob. 2021 (2021), no.22, 15 pages. [21] A. Khaleghi and A. Razani, Solutions to a (p(x); q(x))-biharmonic elliptic problem on a bounded domain, Bound. Value Prob. 2023 (2023), 53. [22] O. Kovacik and J. Rakosnik, On spaces Lp(x) and W1,p(x), Czech. Math. J. 41 (1991), 592–618. [23] J.L. Lions, Quelque Methodes de Resolution des Problemes aux Limites Non Lineaires, Paris: Dunod, Gauthier- Villars 1969. [24] M. Mihailescu, V. Radulescu, A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids, Proc. Roy. Soc. London Ser. A 462 (2006), 2625–2641. [25] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math., vol. 1034, Springer-Verlag, Berlin, 1983. [26] C. Pfeiffer, C.Mavroidis, Y. Bar-Cohen, and B. Dolgin, Electrorheological fluid based force feedback device, Proc. 1999 SPIE Telemanipulator and Telepresence Technologies VI Conf., vol. 3840, Boston, MA, 1999. [27] A. Razani, Entire weak solutions for an anisotropic equation in the Heisenberg group, Proc. Amer. Math. Soc. 151 (2023), no. 11. [28] A. Razani, Non-existence of solution of Haraux-Weissler equation on a strictly star-shaped domain, Miskolc Math. Notes 24 (2023), no. 1, 395–402, [29] A. Razani and G.M. Figueiredo, A positive solution for an anisotropic p£q-Laplacian, Discrete Contin. Dyn. Syst. Ser. S 16 (2023), no. 6, 1629–1643. [30] S. Samko and B. Vakulov, Weighted Sobolev theorem with variable exponent for spatial and spherical potential operators, J. Math. Anal. Appl. 310 (2005), 229-246. [31] D. Zhao, W.J. Qiang, and X.L. Fan, On generalized Orlicz spaces Lp(x), J. Gansu Sci. 9 (1996), no. 2, 1–7. | ||
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