On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces

References

[1] A. Abbassi, C. Allalou and A. Kassidi, Existence of weak solutions for nonlinear p-elliptic problem by topological degree, Nonlinear Dyn. Syst. Theory 20 (2020), no. 3, 229–241. Search in Google Scholar

[2] A. Abbassi, C. Allalou and A. Kassidi, Existence results for some nonlinear elliptic equations via topological degree methods, J. Elliptic Parabol. Equ. 7 (2021), no. 1, 121–136. 10.1007/s41808-021-00098-wSearch in Google Scholar

[3] L. Boccardo, F. Murat and J.-P. Puel, Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Mat. Pura Appl. (4) 152 (1988), 183–196. 10.1007/BF01766148Search in Google Scholar

[4] L. Boccardo, F. Murat and J.-P. Puel, L ∞ estimate for some nonlinear elliptic partial differential equations and application to an existence result, SIAM J. Math. Anal. 23 (1992), no. 2, 326–333. 10.1137/0523016Search in Google Scholar

[5] A. C. Cavalheiro, L ∞ -solutions for some nonlinear degenerate elliptic equations, Int. J. Differ. Equ. 2011 (2011), Article ID 356356. 10.1155/2011/356356Search in Google Scholar

[6] A. C. Cavalheiro, Existence results for a class of nonlinear degenerate elliptic equations, Moroccan J. Pure Appl. Anal. 5 (2019), no. 2, 164–178. 10.2478/mjpaa-2019-0012Search in Google Scholar

[7] F. Chiarenza, Regularity for solutions of quasilinear elliptic equations under minimal assumptions, Potential Anal. 4 (1995), 325–334. 10.1007/978-94-011-0085-4_2Search in Google Scholar

[8] P. Drábek, A. Kufner and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, De Gruyter Ser. Nonlinear Anal. Appl. 5, Walter de Gruyter, Berlin, 1997. 10.1515/9783110804775Search in Google Scholar

[9] E. B. Fabes, C. E. Kenig and R. P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), no. 1, 77–116. 10.1080/03605308208820218Search in Google Scholar

[10] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam, 1985. Search in Google Scholar

[11] S. Heidari and A. Razani, Infinitely many solutions for nonlocal elliptic systems in Orlicz–Sobolev spaces, Georgian Math. J. 29 (2022), no. 1, 45–54. 10.1515/gmj-2021-2110Search in Google Scholar

[12] J. Heinonen, T. Kilpeläinen and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Math. Monogr., Oxford University, New York, 1993. Search in Google Scholar

[13] A. Kufner, Weighted Sobolev Spaces, John Wiley & Sons, New York, 1985. Search in Google Scholar

[14] A. Kufner and B. Opic, How to define reasonably weighted Sobolev spaces, Comment. Math. Univ. Carolin. 25 (1984), no. 3, 537–554. Search in Google Scholar

[15] M. Makvand Chaharlang and A. Razani, Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition, Georgian Math. J. 28 (2021), no. 3, 429–438. 10.1515/gmj-2019-2077Search in Google Scholar

[16] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. 10.1090/S0002-9947-1972-0293384-6Search in Google Scholar

[17] B. Muckenhoupt, The equivalence of two conditions for weight functions, Studia Math. 49 (1973/74), 101–106. 10.4064/sm-49-2-101-106Search in Google Scholar

[18] M. E. Ouaarabi, A. Abbassi and C. Allalou, Existence result for a Dirichlet problem governed by nonlinear degenerate elliptic equation in weighted Sobolev spaces, J. Elliptic Parabol. Equ. 7 (2021), no. 1, 221–242. 10.1007/s41808-021-00102-3Search in Google Scholar

[19] M. E. Ouaarabi, A. Abbassi and C. Allalou, Existence result for a general nonlinear degenerate elliptic problems with measure datum in weighted Sobolev spaces, Int. J. Optim. Appl. 1 (2021), no. 2, 1–9. 10.1007/s41808-021-00102-3Search in Google Scholar

[20] M. E. Ouaarabi, A. Abbassi and C. Allalou, Existence and uniqueness of weak solution in weighted Sobolev spaces for a class of nonlinear degenerate elliptic problems with measure data, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 1, 2635–2653. 10.1007/978-3-031-12416-7_24Search in Google Scholar

[21] M. E. Ouaarabi, C. Allalou and A. Abbassi, On the Dirichlet Problem for some Nonlinear Degenerated Elliptic Equations with Weight, 7th International Conference on Optimization and Applications (ICOA), IEEE Press, Piscataway (2021), 1–6. 10.1109/ICOA51614.2021.9442620Search in Google Scholar

[22] K. R. Rajagopal and M. Růžička, Mathematical modeling of electrorheological materials, Contin. Mech. Thermodyn. 13 (2001), no. 1, 59–78. 10.1007/s001610100034Search in Google Scholar

[23] M. Růžička, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math. 1748, Springer, Berlin, 2000. 10.1007/BFb0104029Search in Google Scholar

[24] B. O. Turesson, Nonlinear Potential Theory and Weighted Sobolev Spaces, Lecture Notes in Math. 1736, Springer, Berlin, 2000. 10.1007/BFb0103908Search in Google Scholar

[25] E. Zeidler, Nonlinear Functional Analysis and its Applications. II/B. Nonlinear Monotone Operators, Springer, New York, 1990. 10.1007/978-1-4612-0981-2Search in Google Scholar