American Journal of Mathematics and Statistics

American Journal of Mathematics and Statistics is to publish well-written original research articles and studies describing the latest research and developments in the field of mathematics and statistics. This is a broad-based journal covering all branches of mathematics, statistics and interdisciplinary research.

## Abdelmoujib Benkirane

Editorial Board Member of American Journal of Mathematics and Statistics

Professor, University of Fez, Morocco

Research Areas

Pure and Applied Mathematics (Nonlinear Pde, Function Spaces)

### Education

 1988 Ph.D University of Nancy

### Experience

 1992-present FSDM, Fez, since 1992 Professor, Courses of all subjects of analysis of the first year until the last license year. Courses on Sobolev spaces and EDP in the third cycle. 1988-1992 Faculty of sciences (FSDM) of Fez, Lecturer Professor, Topology, differential calculus, distributions, Analysis MP2 1980-1988 Ecole normale supérieure (ENS) of Fez.Assistant Professor in Mathematics: Analysis course of MP1 and MP2, Topology and Distributions 1978-1979 University of Nancy I, Assistant Professor.Analysis, section SM1

### Publications: Conferences/Workshops/Symposiums/Journals/Books

 [1] Benkirane, A.; Gossez, J.-P. An approximation theorem in higher order Orlicz-Sobolev spaces and applications. Studia Math. 92(1989), no. 3, 231--255. [2] Benkirane, A. Approximations de type Hedberg dans les espaces $W\sp mL\log L(\Omega)$ et applications. (French) [Hedberg-type approximations in the spaces $W\sp mL\log L(\Omega)$ and applications] Ann. Fac. Sci. Toulouse Math. (5) 11 (1990), no. 2, 67-78. [3] Benkirane, A. Inegalites d'interpolation dans les espaces de Sobolev-Orlicz. (French) [Interpolation inequalities in Sobolev-Orlicz spaces] Bull. Soc. Math. Belg. Ser. B 42 (1990), no. 3, 285--294. [4] Aissaoui, N.; Benkirane, A. Potentiel non lineaire dans les espaces d'Orlicz. (French) [Nonlinear potential in Orlicz spaces] Ann. Sci. Math. Quebec 18 (1994), no. 2, 105--118. [5] Aissaoui, N.; Benkirane, A. Capacites dans les espaces d'Orlicz. (French) [Capacities in Orlicz spaces] Ann. Sci. Math. Quebec 18 (1994), no. 1, 1--23. [6] Benkirane, A. A theorem of H. Brezis and F. E. Browder type in Orlicz spaces and application. Nonlinear partial differential equations (Fès, 1994), 10--16, Pitman Res. Notes Math. Ser., 343, Longman, Harlow, 1996. [7] Benkirane, A.; Elmahi, A. Almost everywhere convergence of the gradients of solutions to elliptic equations in Orlicz spaces and application. Nonlinear Anal. 28 (1997), no. 11, 1769--1784. [8] Benkirane, A.; Elmahi, A. Strongly nonlinear elliptic unilateral problems having natural growth terms and $L\sp 1$ data. Rend. Mat. Appl. (7) 18 (1998), no. 2, 289--303. [9] Benkirane, A.; Elmahi, A. An existence theorem for a strongly nonlinear elliptic problem in Orlicz spaces. Nonlinear Anal. 36 (1999), no. 1, Ser. A: Theory Methods, 11--24. [10] Benkirane, A.; Kbiri Alaoui, M. Sur certaines equations elliptiques non linearires á second membre mesure. (French) [Certain nonlinear elliptic equations with right-hand-side measures] Forum Math. 12 (2000), no. 4, 385--395. [11] Azroul, E.; Benkirane, A.; Tienari, M. On the regularity of solutions to the Poisson equation in Orlicz-spaces. Bull. Belg. Math. Soc. Simon Stevin 7 (2000), no. 1, 1—12 [12] Benkirane, A.; Elmahi, A. A strongly nonlinear elliptic equation having natural growth terms and $L\sp 1$ data. Nonlinear Anal. 39 (2000), no. 4, Ser. A: Theory Methods, 403--411. [13] Akdim, Y.; Azroul, E.; Benkirane, A. Existence of solutions for quasilinear degenerate elliptic equations. Electron. J. Differential Equations 2001, No. 71, 19 pp. (electronic). [14] Benkirane, A.; Kbiri Alaoui, M. Existence of solutions of strongly nonlinear elliptic equations in $R\sp N$. Rev. Mat. Complut. 14 (2001), no. 2, 505--521. [15] Azroul, E.; Benkirane, A. On a necessary condition in the calculus of variations in Orlicz-Sobolev spaces. Math. Slovaca 51 (2001), no. 1, 93--105. [16] Akdim, Youssef; Azroul, Elhoussine; Benkirane, Abdelmoujib. Strongly nonlinear degenerated elliptic unilateral problems via convergence of truncations. Proceedings of the 2002 Fez Conference on Partial Differential Equations, 25--39 (electronic), Electron. J. Differ. Equ. Conf., 9, Southwest Texas State Univ., San Marcos, TX, 2002. MR1976683 (2004d:35089) [17] Aharouch, Lahsen; Azroul, Elhoussine; Benkirane, Abdelmoujib. On the $L\sp \infty$-regularity of solutions of nonlinear elliptic equations in Orlicz spaces. Proceedings of the 2002 Fez Conference on Partial Differential Equations, 1--8 (electronic), Electron. J. Differ. Equ. Conf., 9, Southwest Texas State Univ., San Marcos, TX, 2002. MR1976681 (2004c:35108) [18] Proceedings of the 2002 Fez Conference on Partial Differential Equations. Held at the University Sidi Mohamed Ben Abdellah, Fez, June 6–8, 2002. Edited by Abdelmoujib Benkirane and Abdelfattah Touzani. Electronic Journal of Differential Equations Conference, 9. Southwest Texas State University, San Marcos, TX, 2002. front matter+220 pp. (electronic). MR1976680 (2003m:35005) [19] Benkirane, A.; Bennouna, J. Existence of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms in Orlicz spaces. Partial differential equations, 125--138, Lecture Notes in Pure and Appl. Math., 229, Dekker, New York, 2002. MR1913325 (2003b:35071) [20] Benkirane, A.; Bennouna, J. Existence of entropy solutions for some nonlinear problems in Orlicz spaces. Abstr. Appl. Anal. 7 (2002), no. 2, 85--102. MR1891032 (2003e:35074) [21] Benkirane, A.; Elmahi, A.; Meskine, D. An existence theorem for a class of elliptic problems in $L\sp 1$ . Appl. Math. (Warsaw) 29 (2002), no. 4, 439--457. MR1948425 (2003k:35059) [22] Benkirane, A.; Elmahi, A.; Meskine, D. On the limit of some penalized problems involving increasing powers. Asymptot. Anal. 36 (2003), no. 3-4, 303--317. [23] Benkirane, A.; Elmahi, A.; Meskine, D. On the limit of some nonlinear elliptic problems. Arch. Inequal. Appl. 1 (2003), no. 2, 20--219. [24] Akdim, Youssef; Azroul, Elhoussine; Benkirane, Abdelmoujib. Existence of solution for quasilinear degenerated elliptic unilateral problems. Ann. Math. Blaise Pascal 10 (2003), no. 1, 1--20. [25] Benkirane, A.; Bennouna, J. Existence and uniqueness of solution of unilateral problems with $L\sp 1$-data in Orlicz spaces. Ital. J. Pure Appl. Math. No. 16 (2004), 87--102. [26] Akdim, Youssef; Benkirane, Abdelmoujib; Rhoudaf, Mohamed. Leray Lions degenerated problem with general growth condition. Proceedings of the 2005 Oujda International Conference on Nonlinear Analysis, 73--81 (electronic), Electron. J. Differ. Equ. Conf., 14, Southwest Texas State Univ., San Marcos, TX, 2006. MR2316105 (2008c:35054) [27] Aharouch, L.; Azroul, E.; Benkirane, A. Quasilinear degenerated equations with $L\sp 1$ datum and without coercivity in perturbation terms. Electron. J. Qual. Theory Differ. Equ. 2006, No. 19, 18 pp. (electronic). MR2263078 (2007e:35066) [28] Aharouch, L.; Benkirane, A.; Rhoudaf, M. Strongly nonlinear elliptic variational unilateral problems in Orlicz space. Abstr. Appl. Anal. 2006, Art. ID 46867, 20 pp. [29] Benkirane, Abdelmoujib; Youssfi, Ahmed. Regularity for solutions of nonlinear elliptic equations with degenerate coercivity. Ric. Mat. 56 (2007), no. 2, 241--275. MR2358067 (2008i:35065) [30] Benkirane, A.; Chrif, M.; El Manouni, S. Existence results for strongly nonlinear elliptic equations of infinite order. Z. Anal. Anwend. 26 (2007), no. 3, 303--312. MR2322835 (2009d:35056) [31] Benkirane, Abdelmoujib; Youssfi, Ahmed. Existence of bounded solutions for a class of strongly nonlinear elliptic equations in Orlicz-Sobolev spaces. Aust. J. Math. Anal. Appl. 5 (2008), no. 1, Art. 7, 26 pp. [32] Aharouch, L.; Benkirane, A.; Rhoudaf, M. Existence results for some unilateral problems without sign condition with obstacle free in Orlicz spaces. Nonlinear Anal. 68 (2008), no. 8, 2362--2380. [33] Benkirane, A.; Youssfi, A.; Meskine, D. Bounded solutions for nonlinear elliptic equations with degenerate coercivity and data in an $L\log L$ . Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 2, 369--375. MR2424118 (2009k:35062) [34] Benkirane, Abdelmoujib; Youssfi, Ahmed. Regularizing effects of some lower order terms in non-uniformly nonlinear elliptic equations. Ric. Mat. 58 (2009), no. 2, 185--205. MR2570587 (2011a:35126) [35] Benkirane, A.; Chrif, M.; El Manouni, S. Strongly nonlinear problem of infinite order with $L\sp 1$ data. Electron. J. Qual. Theory Differ. Equ. 2009, No. 15, 12 pp. MR2486658 (2010d:35063) [36] Azroul, E.; Benkirane, A.; Rhoudaf, M. On some strongly nonlinear elliptic problems in $L\sp 1$-data with a nonlinearity having a constant sign in Orlicz spaces via penalization methods. Aust. J. Math. Anal. Appl. 7 (2010), no. 1, Art. 5, 25 pp. [37] Aharouch, L.; Benkirane, A.; Bennouna, J.; Touzani, A. Existence and uniqueness of solutions of some nonlinear equations in Orlicz spaces and weighted Sobolev spaces. Recent developments in nonlinear analysis, 170--180, World Sci. Publ., Hackensack, NJ, 2010. MR2668595 (2011g:35103) [38] Benkirane, A.; Benouna, J.; Rhoudaf, M. Some remarks on a sign condition for perturbations of nonlinear problems. Recent developments in nonlinear analysis, 30--42, World Sci. Publ., Hackensack, NJ, 2010. MR2668587 [39] Benkirane, A.; Chrif, M.; El Manouni, S. Nonlinear elliptic equations of infinite order. Recent developments in nonlinear analysis, 17--29, World Sci. Publ., Hackensack, NJ, 2010. MR2668586 (2011g:35105) [40] A. Benkirane, J. Douieb, M. Ould Mohamedhen Val An approximation theorem in Musielak-Orlicz-Sobolev spaces COMMENTATIONES MATHEMATICAE Vol. 51, No. 1 (2011), 109-120 [41] Azroul, E.; Benkirane, H.Radwan, A.; Rhoudaf, M. A theorem of Hedberg type in Weighted Sobolev spaces and applications. (in correction) To appear in "Journal of Differential Equations"