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Revista Colombiana de Matemáticas

versão impressa ISSN 0034-7426

Rev.colomb.mat. vol.55 no.1 Bogotá jan./jun. 2021  Epub 17-Nov-2021 

Original articles

Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces

Abdeslam Talha1  * 

Mohamed Saad Bouh Elemine Vall2 

1 Univ. Hassan I, Settat, Morocco

2 University of Nouakchott Al Aasriya, Nouakchott, Mauritania


In this paper, we prove the existence of solutions to an elliptic problem containing two lower order terms, the first nonlinear term satisfying the growth conditions and without sign conditions and the second is a continuous function on R.

Keywords: Poincaré inequality; Musielak-Orlicz-Sobolev Spaces; Unilateral problems; Measurable obstacle; Lower order term


En este artículo, demostramos la existencia de soluciones a un problema diferencial elíptico que contiene dos términos de bajo orden, donde el primer término no lineal satisface condiciones de crecimiento sin restricciones en el signo y el segundo es una función continua sobre R.

Palabras clave: desigualdad de Poincaré; espacios Musielak-Orlicz-Sobolev; problemas unilaterales; obstáculo medible; Término de orden inferior

Texto PDF


1. L. Aharouch, A. Benkirane, and M. Rhoudaf, Strongly nonlinear elliptic variational unilateral problems in orlicz spaces, Abstr. Appl. Anal. Art. ID 46867(20), (2006), 1-20. [ Links ]

2. L. Aharouch, J. Bennouna, and A. Touzani, Existence of Renormalized Solution of Some Elliptic Problems in Orlicz Spaces, Rev. Mat. Complut. 22 (2009), no. 1, 91-110. [ Links ]

3. M. Avci and A. Pankov, Multivalued elliptic operators with nonstandard growth, Advances in Nonlinear Analysis 0 (2016), no. 0, 1-14. [ Links ]

4. E. Azroul, H. Redwane, and C. Yazough, Stronglyn onlinear non homogeneous elliptic unilateral problems with l1 data and no sign conditions, Electron. J. Differ. Equ. 79 (2012), 1-20. [ Links ]

5. M. Bendahmane and P. Wittbold, Renormalized solutions for nonlinear elliptic equations with variable exponents and l1 data, Nonlinear Anal. 70 (2009), 567-583. [ Links ]

6. A. Benkirane and J. Bennouna, Existence of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms in orlicz spaces, In: Partial Differential Equations. Lect. Notes Pure Appl. Math. Dekker, New York 229 (2002), no. 0, 251-138. [ Links ]

7. A. Benkirane and M. Sidi El Vally (Ould Mohamedhen Val), Some approximation properties in Musielak-Orlicz-Sobolev spaces, Thai J. Math. 10 (2012), no. 2, 371-381. [ Links ]

8. A. Benkirane and M. Sidi El Vally (Ould Mohamedhen Val), Variational inequalities in Musielak-Orlicz-Sobolev spaces, Bull. Belg. Math. Soc. Simon Stevin 21 (2014), 787-811. [ Links ]

9. L. Boccardo, S. Segura de león, and C. Trombetti, Bounded and unbounded solutions for a class of quasi{linear elliptic problems with a quadratic gradient term, J. Math. Pures Appl. 9 (2001), no. 80, 919-940. [ Links ]

10. L. Boccardo , F. Murat, and J. P. Puel, l1 estimate for some nonlinear elliptic partial differential equations and application to an existence result, SIAM J. Math. Anal. 2 (1992), 326-333. [ Links ]

11. Y. Chen, S. Levine, and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. (electronic) 66 (2006), no. 4, 1383-1406. [ Links ]

12. F. Giannetti and A. Passarelli di Napoli, Regularity results for a new class of functionals with nonstandard growth conditions, J. Differential Equations 254 (2013), no. 3, 1280-1305. [ Links ]

13. J.-P. Gossez , Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Amer. Math. Soc. 190 (1974), 163-205. [ Links ]

14. J.-P. Gossez , A strongly nonlinear elliptic problem in orlicz-sobolev spaces, Proc. Symp. Pure Math. 45 (1986), 455-462. [ Links ]

15. J.-P. Gossez and V. Mustonen, Variational inequalities in Orlicz-Sobolev spaces, Nonlinear Anal., Theory Methods Appl. 11 (1987), 379-392. [ Links ]

16. P. Gwiazda and A. Swierczewska-Gwiazda, On non-newtonian fluids with a property of rapid thickening under different stimulus, Math. Models Methods Appl. Sci. 18 (2008), no. 7, 1073-1092. [ Links ]

17. P. Gwiazd a and A. Swierczewska-Gwiazda , On steady non-newtonian fluids with growth conditions in generalized orlicz spaces, Topol. Methods Nonlinear Anal . 32 (2008), no. 1, 103-114. [ Links ]

18. P. Harjulehto, P. Hastö, V. Latvala, and O. Toivanen, Critical variable exponent functionals in image restoration, Appl. Math. Lett. 26 (2013), no. 1, 56-60. [ Links ]

19. B. Karim, B. Zerouali, and O. Chakrone, Existence and Multiplicity Results for Steklov Problems with p(()-Growth Conditions, Bull. Iran. Math. Soc. 44 (2018), 819-836. [ Links ]

20. M. Ait Khellou and A. Benkirane, Elliptic inequalities with L1 data in Musielak-Orlicz spaces, Monatsh Math 183 (2017), 1-33. [ Links ]

21. J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034, Springer, Berlin, 1983. [ Links ]

22. A. Porretta, Nonlinear equations with natural growth terms and measure data, Electron. J. Differ. Equ. Conf. 9 (2002), 181-202. [ Links ]

23. A. Porretta, Uniqueness of solutions for some nonlinear Dirichlet problems, NoDEA Nonlinear differ. equ. appl. 11 (2004), 407-430. [ Links ]

24. A. Talha, A. Benkirane , and M. S. B. Elemine Vall, Entropy solutions for nonlinear parabolic inequalities involving measure data in musielak-orliczsobolev spaces, Bol. Soc. Paran. Mat. 36 (2018), no. 2, 199-230. [ Links ]

Received: April 17, 2020; Accepted: March 15, 2021

* Correspondencia: Abdeslam Talha, Laboratoire MISI, Laboratoire MISI, FST Settat, Univ. Hassan I, 26000 Settat, Morocco Correo electrónico: DOI:

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