Existence results for some anisotropic possible singular problems via the sub-supersolution method

Authors

  • Abdelrachid EL AMROUSS Department of Mathematics and Computer, Laboratory MAO, Faculty of Science, Mohammed the 1st University, Oujda, Morocco. Email: elamrouss@hotmail.com https://orcid.org/0000-0003-3536-398X
  • Hamidi ABDELLAH Department of Mathematics and Computer, Laboratory MAO, Faculty of Science, Mohammed the 1st University, Oujda, Morocco. Email: abdellah2hamidi1@gmail.com
  • Kissi FOUAD Faculty of Legal Economic and Social Sciences, Laboratory of Mathematics MAO, Mohammed 1st University, Oujda, Morocco. Email: kissifouad@hotmail.com https://orcid.org/0000-0002-0017-265X

DOI:

https://doi.org/10.24193/subbmath.2024.4.10

Keywords:

Anisotropic problem, singular nonlinearity, sub-super solution, strong maximum principle

Abstract

Using the sub-super solution method, we prove the existence of the solutions for the following anisotropic problem with singularity, where Ω⊂RN is a bounded domain with smooth boundary and a given singular nonlinearity f : Ω×(0,∞)⟶[0,∞) f : Ω×(0,∞)⟶[0,∞).

Mathematics Subject Classification (2010): 35B50, 35B51, 35J75, 35J60.

References

1. Alves, C.O., El Hamidi, A., Existence of solution for a anisotropic equation with critical exponent, Differential and Integral Equations., (2008), 25-40.

2. Boukarabila, Y.O., Miri, S.E.H., Anisotropic system with singular and regular nonlinearities, Complex Variables and Elliptic Equations., 65(2020), no. 4, 621-631.

3. Ciani, S., Figueiredo, G. M., Suarez, A., Existence of positive eigenfunctions to an anisotropic elliptic operator via the sub-supersolution method, Archiv der Mathematik, 116(2021), no. 1, 85-95.

4. Coclite, G.M., Coclite, M.M., On a Dirichlet problem in bounded domains with singular nonlinearity, Discrete and Continuous Dynamical Systems, 33(2013), no. 11-12, 4923- 4944.

5. Diaz, J.I., Nonlinear partial differential equations and free boundaries, Elliptic Equations, Research Notes in Math., 106(1985), 323.

6. Di Castro, A., Existence and regularity results for anisotropic elliptic problems, Advanced Nonlinear Studies, 9(2009), no. 2, 367-393.

7. Di Castro, A., Local Holder continuity of weak solutions for an anisotropic elliptic equation, Nonlinear Differ. Equ. Appl., 20(2013), 463-486.

8. Di Castro, A., Montefusco, E., Nonlinear eigenvalues for anisotropic quasilinear degenerate elliptic equations, Nonlinear Analysis: Theory, Methods & Applications, 70(2009), no. 11, 4093-4105.

9. Dinca, G., Jebelean, P., Mawhin, J., Variational and topological methods for Dirichlet problems with p-Laplacian, Portugaliae Mathematica, 58(2001), no. 3, 339.

10. Dos Santos, G.C., Figueiredo, G.M., Tavares, L.S., Existence results for some anisotropic singular problems via sub-supersolutions, Milan Journal of Mathematics, 87(2019), 249- 272.

11. El Amrouss, A., El Mahraoui, A., Existence and multiplicity of solutions for anisotropic elliptic equation, Boletim da Sociedade Paranaense de Matematica., 40(2022).

12. Fan, X., Zhao, D., On the spaces Lp(x)(Ω) and Wm, p(x)(Ω), Journal of Mathematical Analysis and Applications, 263(2001), no. 2, 424-446.

13. Fragala, I., Gazzola, F., Kawohl, B., Existence and nonexistence results for anisotropic quasilinear elliptic equations, Annales de l’Institut Henri Poincar´e C, 21(2004), no. 5, 715-734.

14. Fulks, W., Maybee, J.S., A singular non-linear equation, Osaka Mathematical Journal, 12(1960), no. 1, 1-19.

15. Henriquez-Amador, J., Valez-Santiago, A., Generalized anisotropic neumann problems of Ambrosetti-Prodi type with nonstandard growth conditions, Journal of Mathematical Analysis and Applications, 494(2021), no. 2, 124668.

16. Lair, A.V., Shaker, A.W., Classical and weak solutions of a singular semilinear elliptic problem, Journal of Mathematical Analysis and Applications, 211(1997), no. 2, 371-385.

17. Leggat, A.R., Miri, S.E.H., Anisotropic problem with singular nonlinearity, Complex Variables and Elliptic Equations, 61(2016), no. 4, 496-509.

18. Lipkova, J., Angelikopoulos, P., Wu, S., Alberts, E., Wiestler, B., Diehl, C., Menze, B., Personalized radiotherapy design for glioblastoma: Integrating mathematical tumor models, multimodal scans, and bayesian inference, IEEE Transactions on Medical Imaging, 38(2019), no. 8, 1875-1884.

19. Loc, N.H., Schmitt, K., Boundary value problems for singular elliptic equations, The Rocky Mountain Journal of Mathematics, 41(2011), no. 2, 555-572.

20. Miri, S.E.H., On an anisotropic problem with singular nonlinearity having variable exponent, Ricerche di Matematica, 66(2017), 415-424.

21. Mohammed, A., Positive solutions of the p-laplace equation with singular nonlinearity, Journal of Mathematical Analysis and Applications, 352(2009), no. 1, 234-245.

22. Perera, K., Silva, E.A., Existence and multiplicity of positive solutions for singular quasilinear problems, Journal of Mathematical Analysis and Applications, 323(2006), no. 2, 1238-1252.

23. Rajagopal, K.R., Ruzicka, M., Mathematical modeling of electrorheological materials, Continuum Mechanics and Thermodynamics, 13(2001), no. 1, 59-78.

24. Ruzicka, M., Electrorheological Fluids: Modeling and Mathematical Theory, Springer, 2007.

25. Zhang, Z., Cheng, J., Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems, Nonlinear Analysis: Theory, Methods and Applications, 57(2004), no. 3, 473-484.

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Published

2024-12-13

How to Cite

EL AMROUSS, A., ABDELLAH, H., & FOUAD, K. (2024). Existence results for some anisotropic possible singular problems via the sub-supersolution method. Studia Universitatis Babeș-Bolyai Mathematica, 69(4), 849–862. https://doi.org/10.24193/subbmath.2024.4.10

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