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

• Autores: Abdeslam Talha, Mohamed Saad Bouh Elemine Vall
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 55, Nº. 1, 2021, págs. 43-70
• Idioma: inglés
• DOI: 10.15446/recolma.v55n1.99098
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • L. Aharouch, A. Benkirane, and M. Rhoudaf, Strongly nonlinear elliptic variational unilateral problems in orlicz spaces, Abstr. Appl. Anal....
  • L. Aharouch, J. Bennouna, and A. Touzani, Existence of Renormalized Solution of Some Elliptic Problems in Orlicz Spaces, Rev. Mat. Complut....
  • 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,...
  • M. Bendahmane and P. Wittbold, Renormalized solutions for nonlinear elliptic equations with variable exponents and l1 data, Nonlinear Anal....
  • A. Benkirane and J. Bennouna, Existence of renormalized solutions for some elliptic problems involving derivatives of nonlinear terms in orlicz...
  • A. Benkirane and M. Sidi El Vally (Ould Mohamedhen Val), Some approximation properties in Musielak-Orlicz-Sobolev spaces, Thai J. Math. 10...
  • A. Benkirane and M. Sidi El Vally (Ould Mohamedhen Val), Variational inequalities in Musielak-Orlicz-Sobolev spaces, Bull. Belg. Math. Soc....
  • L. Boccardo, S. Segura de león, and C. Trombetti, Bounded and unbounded solutions for a class of quasi{linear elliptic problems with a quadratic...
  • L. Boccardo, F. Murat, and J. P. Puel, l1 estimate for some nonlinear elliptic partial differential equations and application to an existence...
  • Y. Chen, S. Levine, and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. (electronic) 66 (2006),...
  • F. Giannetti and A. Passarelli di Napoli, Regularity results for a new class of functionals with nonstandard growth conditions, J. Differential...
  • J.-P. Gossez, Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Amer. Math....
  • , A strongly nonlinear elliptic problem in orlicz-sobolev spaces, Proc. Symp. Pure Math. 45 (1986), 455-462.
  • J.-P. Gossez and V. Mustonen, Variational inequalities in Orlicz-Sobolev spaces, Nonlinear Anal., Theory Methods Appl. 11 (1987), 379-392.
  • P. Gwiazda and A. Swierczewska-Gwiazda, On non-newtonian fluids with a property of rapid thickening under different stimulus, Math. Models...
  • P. Gwiazda and A. Swierczewska-Gwiazda, On steady non-newtonian fluids with growth conditions in generalized orlicz spaces, Topol. Methods...
  • P. Harjulehto, P. Hastö, V. Latvala, and O. Toivanen, Critical variable exponent functionals in image restoration, Appl. Math. Lett. 26 (2013),...
  • B. Karim, B. Zerouali, and O. Chakrone, Existence and Multiplicity Results for Steklov Problems with p(.)-Growth Conditions, Bull. Iran. Math....
  • M. Ait Khellou and A. Benkirane, Elliptic inequalities with L1 data in Musielak-Orlicz spaces, Monatsh Math 183 (2017), 1-33.
  • J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034, Springer, Berlin, 1983.
  • 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.
  • A. Talha, A. Benkirane, and M. S. B. Elemine Vall, Entropy solutions for nonlinear parabolic inequalities involving measure data in musielak-orliczsobolev...