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Weak solution to a class of nonlinear degenerate weighted elliptic p(u)-Laplacian problem | ||
International Journal of Nonlinear Analysis and Applications | ||
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 27 مرداد 1404 اصل مقاله (419.84 K) | ||
نوع مقاله: Review articles | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.33441.4985 | ||
نویسندگان | ||
El Mehdi Hassoune1؛ Ahmed Jamea* 1، 2؛ Mohamed Laghdir1؛ Adnane Kaddiri1 | ||
1Laboratoire LITE, Faculté des Sciences, Université Chouaib Doukkali El Jadida, Morocco | ||
2CRMEF Casablanca-Settat, S.P. El Jadida,El Jadida, Morocco | ||
تاریخ دریافت: 14 اسفند 1402، تاریخ بازنگری: 02 فروردین 1404، تاریخ پذیرش: 04 فروردین 1404 | ||
چکیده | ||
In this work, our objective is to prove the existence and uniqueness of weak solutions to a class of nonlinear degenerate weighted elliptic p(u)-Laplacian problem with Dirichlet-type and $L^{\infty}$ data. For this, we utilise some results from Sobolev spaces with weighted and variable exponents, as well as theorems such as the Minty-Browder theorem. | ||
کلیدواژهها | ||
Nonlinear elliptic problem؛ weak solution؛ uniqueness؛ weighted Sobolev space | ||
مراجع | ||
[1] A. Abbassi, E. Azroul, and A. Barbara, Degenerate p(x)-elliptic equation with second member in L1, Adv. Sci. Technol. Engin. Syst. J. 10 (2017), no. 5, 45–54. [2] A. Abassi, A. El Hachimi, and A. Jamea, Entropy solutions to nonlinear Neumann problems with L1-data, Int. Math. Statist. 2 (2008), no. S8, 4–17. [3] F. Bay, V. Labbe, Y. Favennec, and J.L. Chenot, A numerical model for induction heating processes coupling electromagnetism and thermomechanics, Int. J. Numer. Meth. Engin. 58 (2003), no. 6, 839-867. [4] A.C. Cavalheiro, Weighted Sobolev spaces and degenerate elliptic equations, Bol. Soc. Paranaense Mate. 26 (2008), 1085–1111. [5] M. Chipot and H.B. De Oliveira, Some results on the p(u)-Laplacian problem, Math. Ann. 375 (2019), no. 1, 283–306. [6] J.I. Diaz and F. De Thelin, On a nonlinear parabolic problem arising in some models related to turbulent flows, SIAM J. Math. Anal. 25 (1994), 1085–1111. [7] L. Diening, P. Harjulehto, P. Hasto, and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponent, Springer, 2011. [8] P. Drabek, A. Kufner, and V. Mustonen, Pseudo-monotonicity and degenerated or singular elliptic operators, Bull. Aust. Math. Soc. 58 (1998), no. 2, 213–221. [9] A. Jamea, A.A. Lamrani, and A. El Hachimi, Existence of entropy solutions to nonlinear parabolic problems with variable exponent and L1-data, Ric. Mate. 67 (2018), no. 2, 785–801. [10] J.L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Etudes Math. 361 (1969). [11] D. Motreanu and A. Razani, Competing anisotropic and Finsler (p,q)-Laplacian problems, Boundary Value Prob[1]lems 2024 (2024), no. 1, 39. [12] M.A. Ragusa, A. Razani, and F. Safari, Existence of radial solutions for a p(x)-Laplacian Dirichlet problem, Adv. Differ. Equ. 2021 (2021), no. 1, 215. [13] A. Razani, Competing Kohn-Spencer Laplacian systems with convection in non-isotropic Folland-Stein space, Complex Variables Elliptic Equ. 70 (2025), no. 4, 667–680. [14] A. Razani and G.M. Figueiredo, On the Fucik spectrum for the p,q-Laplacian, Discrete Cont. Dyn. Syst. Ser. S 16 (2023), no. 11, 3318–3332. [15] M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Vol. 1748, Springer, 2000. [16] A. Sabri, A. Jamea, and H. Talibi Alaoui, Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and L1-data, Commun. Math. 28 (2020), 67–88. [17] A. Sabri, A. Jamea, and H. Talibi Alaoui, Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundary condition in weighted Sobolev spaces, Math. Bohemica 147 (2022), no. 1, 113–129. [18] M. Sanchon and J.M. Urbano, Entropy solutions for the p(x)-Laplace equation, Trans. Amer. Math. Soc. 361 (2009), no. 12, 6387–6405. [19] C. Zhang and X. Zhang, Some further results on the nonlocal p-Laplacian type problems, Proc. Roy. Soc. Edin. Sect. A 151 (2021), no. 3, 953–970. | ||
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