Published

2021-10-18 — Updated on 2021-10-19

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

DOI:

https://doi.org/10.15446/recolma.v55n1.99098

Keywords:

Poincaré inequality, Musielak-Orlicz-Sobolev Spaces, Unilateral problems, Measurable obstacle, Lower order term (en)
desigualdad de Poincaré, espacios Musielak-Orlicz-Sobolev, problemas unilaterales, obstáculo medible, Término de orden inferior (es)

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Authors

  • Abdeslam Talha Univ. Hassan I
  • Mohamed Saad Bouh Elemine Vall University of Nouakchott Al Aasriya

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.

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.

References

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. DOI: https://doi.org/10.1155/AAA/2006/46867

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. DOI: https://doi.org/10.5209/rev_REMA.2009.v22.n1.16319

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

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.

M. Bendahmane and P. Wittbold, Renormalized solutions for nonlinear elliptic equations with variable exponents and l1 data, Nonlinear Anal. 70 (2009), 567-583. DOI: https://doi.org/10.1016/j.na.2007.12.027

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. DOI: https://doi.org/10.1201/9780203910108.ch10

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.

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. DOI: https://doi.org/10.36045/bbms/1420071854

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. DOI: https://doi.org/10.1016/S0021-7824(01)01211-9

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. DOI: https://doi.org/10.1137/0523016

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. DOI: https://doi.org/10.1137/050624522

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. DOI: https://doi.org/10.1016/j.jde.2012.10.011

J.-P. Gossez, Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Amer. Math. Soc. 190 (1974), 163-205. DOI: https://doi.org/10.1090/S0002-9947-1974-0342854-2

J.-P. Gossez, A strongly nonlinear elliptic problem in orlicz-sobolev spaces, Proc. Symp. Pure Math. 45 (1986), 455-462. DOI: https://doi.org/10.1090/pspum/045.1/843579

J.-P. Gossez and V. Mustonen, Variational inequalities in Orlicz-Sobolev spaces, Nonlinear Anal., Theory Methods Appl. 11 (1987), 379-392. DOI: https://doi.org/10.1016/0362-546X(87)90053-8

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. DOI: https://doi.org/10.1142/S0218202508002954

P. Gwiazda 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.

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. DOI: https://doi.org/10.1016/j.aml.2012.03.032

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. DOI: https://doi.org/10.1007/s41980-018-0054-5

M. Ait Khellou and A. Benkirane, Elliptic inequalities with L1 data in Musielak-Orlicz spaces, Monatsh Math 183 (2017), 1-33. DOI: https://doi.org/10.1007/s00605-016-1010-1

J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034, Springer, Berlin, 1983. DOI: https://doi.org/10.1007/BFb0072210

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

A. Porretta, Uniqueness of solutions for some nonlinear Dirichlet problems, NoDEA Nonlinear differ. equ. appl. 11 (2004), 407-430. DOI: https://doi.org/10.1007/s00030-004-0031-y

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. DOI: https://doi.org/10.5269/bspm.v36i2.31818

How to Cite

APA

Talha, A. and Bouh Elemine Vall, M. S. . (2021). Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces. Revista Colombiana de Matemáticas, 55(1), 43–70. https://doi.org/10.15446/recolma.v55n1.99098

ACM

[1]
Talha, A. and Bouh Elemine Vall, M.S. 2021. Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces. Revista Colombiana de Matemáticas. 55, 1 (Oct. 2021), 43–70. DOI:https://doi.org/10.15446/recolma.v55n1.99098.

ACS

(1)
Talha, A.; Bouh Elemine Vall, M. S. . Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces. rev.colomb.mat 2021, 55, 43-70.

ABNT

TALHA, A.; BOUH ELEMINE VALL, M. S. . Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces. Revista Colombiana de Matemáticas, [S. l.], v. 55, n. 1, p. 43–70, 2021. DOI: 10.15446/recolma.v55n1.99098. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/99098. Acesso em: 10 jul. 2024.

Chicago

Talha, Abdeslam, and Mohamed Saad Bouh Elemine Vall. 2021. “Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces”. Revista Colombiana De Matemáticas 55 (1):43-70. https://doi.org/10.15446/recolma.v55n1.99098.

Harvard

Talha, A. and Bouh Elemine Vall, M. S. . (2021) “Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces”, Revista Colombiana de Matemáticas, 55(1), pp. 43–70. doi: 10.15446/recolma.v55n1.99098.

IEEE

[1]
A. Talha and M. S. . Bouh Elemine Vall, “Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces”, rev.colomb.mat, vol. 55, no. 1, pp. 43–70, Oct. 2021.

MLA

Talha, A., and M. S. . Bouh Elemine Vall. “Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces”. Revista Colombiana de Matemáticas, vol. 55, no. 1, Oct. 2021, pp. 43-70, doi:10.15446/recolma.v55n1.99098.

Turabian

Talha, Abdeslam, and Mohamed Saad Bouh Elemine Vall. “Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces”. Revista Colombiana de Matemáticas 55, no. 1 (October 18, 2021): 43–70. Accessed July 10, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/99098.

Vancouver

1.
Talha A, Bouh Elemine Vall MS. Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces. rev.colomb.mat [Internet]. 2021 Oct. 18 [cited 2024 Jul. 10];55(1):43-70. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/99098

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