SciELO - Scientific Electronic Library Online

 
vol.23 número3EXISTENCE OF SOLUTIONS FOR A DISCRETE NON LINEAR EIGENVALUE PROBLEM índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados

Revista

Articulo

Indicadores

Links relacionados

Compartir


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.23 n.3 Antofagasta dic. 2004

http://dx.doi.org/10.4067/S0716-09172004000300007 

 

Proyecciones
Vol. 23, No 3, pp. 293-317, December 2004.
Universidad Católica del Norte
Antofagasta - Chile

EXISTENCE OF SOLUTIONS FOR UNILATERAL PROBLEMS WITH L1 DATA IN ORLICZ SPACES

 

L. AHAROUCH

and

MOHAMED RHOUDAF

University of Sidi Mohamed Ben Abdallah, Maroc

Correspondencia a:


ABSTRACT

This article is concerned with the existence result of the unilateral problem associated to equations of the type

Au + g(x, u,Ñu) = f,

in Orlicz spaces, where f Î L1(W), the term g is a nonlinearity having natural growth and satisfying the sign condition. Some stability and positivity properties of solutions are proved.

Key words and phrases : Orlicz Sobolev spaces, boundary value problems,truncations, unilateral problems.

AMS Classification : 35J60.


References

[1] R. Adams , Sobolev espaces,Academic Press, New York, (1975).        [ Links ]

[2] P. Bénilan, L. Boccardo, T. Gallouet, R. Gariepy, M. Pierre and J. L. Vázquez, An L1-theory of existence and uniqueness of nonlinear elliptic equations., Ann. Scuola Norm. Sup. Pisa 22, pp. 240-273, (1995).        [ Links ]

[3] A. Benkirane , Approximation de type de Hedberg dans les espaces W mLlogL(.) et application, Ann. Fac. Sci. Toulouse. 11, 4 , pp. 67-78, (1990).        [ Links ]

[4] A. Benkirane and A. Elmahi, An existence theorem for a strongly nonlinear elliptic problems in Orlicz spaces, Nonlinear Anal. T. M. A., 36, pp. 11-24, (1999).        [ Links ]

[5] A. Benkirane and A. Elmahi, A strongly nonlinear elliptic equation having natural growth terms and L1 data, Nonlinear Anal. T. M. A., 39, pp. 403-411, (2000).        [ Links ]

[6] A. Benkirane, A. Elmahi, and D. Meskine , An existence theorem for a class of elliptic problems in L1, Applicationes Mathematicae., 29, 4 , pp. 439-457, (2002).        [ Links ]

[7] A. Benkirane and J. P. Gossez, An approximation theorem for higher order Orlicz-Sobolev spaces, Studia Math., 92, pp. 231-255, (1989).        [ Links ]

[8] G. Dalmaso, F. Murat, L. Orsina and A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup Pisa, Cl. Sci. 12, 4, pp. 741-808, (1997).        [ Links ]

[9] A. Elmahi, D. Meskine, Unilateral elliptic problems in L1 with natural growth terms, To appear Nonlinear and convex analysis.,        [ Links ]

[10] M. Fuchs and L. Gongbao, L8-bounds for elliptic equations on Orlicz-Sobolev spaces, Archiv der Mathematik, 72, pp. 293-297, (1999).        [ Links ]

[11] M. Fuchs and G. Seregin, Variational methods for fluids for Prandtl- Eyring type and plastic materials with logarithmic hardening, Preprint No. 476. SFB256, Universit¨at Bonn, Math.Methods Appl. Sci. in press.        [ Links ]

[12] M. Fuchs and G. Seregin, A regurality theory for variational integrals with LlnL-growth, Calc. of Variations , 6, pp. 171-187, (1998).        [ Links ]

 [13] M. Fuchs and G. Seregin, Regurality for solutions of variational problems in the deformation theory of plasticity with logarithmic hardening, Preprint No. 421, SFB256, Universit¨at Bonn.        [ Links ]

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

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

[16] M. A. Krasnosel’skii and Y. B. Rutikii , Convex functions and Orlicz spaces, Noordho. Groningen, (1969).        [ Links ]

[17] A. Porretta , Existence for elliptic equations in L1 having lower order terms with natural growth, Portugal. Math. 57, pp. 179-190, (2000).        [ Links ]

 

Received : March 2004. Accepted : October 2004

 

L. Aharouch
Non Linear Analysis Laboratory
Departement of Mathematics and Informatics
Faculty of Sciences Dhar El Mahraz
University of Sidi Mohamed Ben Abdallah
PB 1796 Fez
Maroc
e-mail : l aharouch@yahoo.fr

and

Mohamed Rhoudaf
Non Linear Analysis Laboratory
Departement of Mathematics and Informatics
Faculty of Sciences Dhar El Mahraz
University of Sidi Mohamed Ben Abdallah
PB 1796 Fez
Maroc
e-mail : rhoudaf mohamed@yahoo.fr

 

Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons