Publicado

2019-01-01

Topological degree methods for a Strongly nonlinear p(x)-elliptic problem

Métodos de grado topológico para un problema p(x)-elíptico fuertemente no lineal

DOI:

https://doi.org/10.15446/recolma.v53n1.81036

Palabras clave:

Strongly nonlinear elliptic problem, Generalized Lebesgue and Sobolev spaces, p(x)-Laplacian, Topological Degree (en)
Problema elíptico fuertemente no lineal, espacios generalizados de Lebesgue y Sobolev, p(x)-Laplaciano, grado topológico (es)

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Autores/as

  • Mustapha Ait Hammou Universidad Sidi Mohamed Ibn Abdellah - Facultad de Ciencias Dhar El Mahraz Fes - Departamento de Matemáticas
  • Elhoussine Azroul Universidad Sidi Mohamed Ibn Abdellah - Facultad de Ciencias Dhar El Mahraz Fes - Departamento de Matemáticas
  • Badr Lahmi Universidad Sidi Mohamed Ibn Abdellah - Facultad de Ciencias Dhar El Mahraz Fes - Departamento de Matemáticas

This article is devoted to study the existence of weak solutions for the strongly nonlinear p(x)-elliptic problem Our technical approach is based on the recent Berkovits topological degree.

Este artículo está dedicado a estudiar la existencia de soluciones débiles para el problema p(x)-elíptico fuertemente no lineal Nuestro enfoque técnico se basa en el reciente grado topologico de Berkovits.

Referencias

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G. Bonanno and A. Chinnì, Discontinuous elliptic problems involving the p(x)-laplacian, Math.Nachr. 284 (2011), no. 5-6, 639-652.

G. Bonanno and A. Chinnì, Multiple solutions for elliptic problems involving the p(x)-laplacian, Matematiche (Catania) 66 (2011), no. 1, 105-113.

G. Bonanno and A. Chinnì, Existence results of infinitely many solutions for p(x)-laplacian elliptic Dirichlet problems, Complex Var. Elliptic Equ. 57 (2012), no. 11, 1233-1246.

K.C. Chang, Critical point theory and applications, Shanghai Scientific and Technology Press, Shanghai, 1986 (english).

O. Kovácik and J. Rákosník, On spaces Lp(x) and W1, p(x), Czechoslovak Math. J. 41 (1991), 592-618.

G. Dai, Infinitely many non-negative solutions for a Dirichlet problem involving p(x)-laplacian, Nonlinear Anal. 71 (2009), 5840-5849.

X. L. Fan and X. Han, Existence and multiplicity of solutions for p(x)- laplacian equations in Rn, Nonlinear Anal. 59 (2004), 173-188.

X.L. Fan and Q.H. Zhang, Existence of solutions for p(x)-laplacian Dirichlet problem, Nonlinear Anal. 52 (2003), 1843-1852.

X.L. Fan and D. Zhao, On the spaces Lp(x) and Wm,p(x), J. Math. Anal. Appl. 263 (2001), 424-446.

P.S. Ilias, Existence and multiplicity of solutions of a p(x)-laplacian equation in a bounded domain, Rev. Roumaine Math. Pures Appl. 52 (2007), no. 6, 639-653.

D. Zhao, W.J. Qiang and X.L. Fan, On generalized Orlicz spaces Lp(x), J. Gansu Sci. 9 (1996), no. 2, 1-7.

M. Ruzicka, Electrorheological fuids: modeling and mathematical theory, Lecture Notes in Mathematics, 1748, Springer-Verlag, Berlin, 2000. MR 1810360, 1986 (English).

Harjulehto P, Hästö P, Koskenoja, Varonen S, The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values, Potential Anal 25 (2006), 205-222.

S.G. Samko, Density of C1 0 (Rn) in the generalized Sobolev spaces Wm,p(x)(Rn), Dokl Akad Nauk 369 (1999), no. 4, 451-454.

E. Zeidler, Nonlinear functional analysis and its applications, II/B: Nonlinear monotone Operators, Springer, New York, 1990 (English).

X. Fan , Q. Zhang and D. Zhaoa, Eigenvalues of p(x)-laplacian Dirichlet problem, J. Math. Anal. Appl. 302 (2005), 306-317.

V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR. Izv. 29 (1987), 33-66.

Cómo citar

APA

Hammou, M. A., Azroul, E. y Lahmi, B. (2019). Topological degree methods for a Strongly nonlinear p(x)-elliptic problem. Revista Colombiana de Matemáticas, 53(1), 27–39. https://doi.org/10.15446/recolma.v53n1.81036

ACM

[1]
Hammou, M.A., Azroul, E. y Lahmi, B. 2019. Topological degree methods for a Strongly nonlinear p(x)-elliptic problem. Revista Colombiana de Matemáticas. 53, 1 (ene. 2019), 27–39. DOI:https://doi.org/10.15446/recolma.v53n1.81036.

ACS

(1)
Hammou, M. A.; Azroul, E.; Lahmi, B. Topological degree methods for a Strongly nonlinear p(x)-elliptic problem. rev.colomb.mat 2019, 53, 27-39.

ABNT

HAMMOU, M. A.; AZROUL, E.; LAHMI, B. Topological degree methods for a Strongly nonlinear p(x)-elliptic problem. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. 1, p. 27–39, 2019. DOI: 10.15446/recolma.v53n1.81036. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/81036. Acesso em: 29 may. 2024.

Chicago

Hammou, Mustapha Ait, Elhoussine Azroul, y Badr Lahmi. 2019. «Topological degree methods for a Strongly nonlinear p(x)-elliptic problem». Revista Colombiana De Matemáticas 53 (1):27-39. https://doi.org/10.15446/recolma.v53n1.81036.

Harvard

Hammou, M. A., Azroul, E. y Lahmi, B. (2019) «Topological degree methods for a Strongly nonlinear p(x)-elliptic problem», Revista Colombiana de Matemáticas, 53(1), pp. 27–39. doi: 10.15446/recolma.v53n1.81036.

IEEE

[1]
M. A. Hammou, E. Azroul, y B. Lahmi, «Topological degree methods for a Strongly nonlinear p(x)-elliptic problem», rev.colomb.mat, vol. 53, n.º 1, pp. 27–39, ene. 2019.

MLA

Hammou, M. A., E. Azroul, y B. Lahmi. «Topological degree methods for a Strongly nonlinear p(x)-elliptic problem». Revista Colombiana de Matemáticas, vol. 53, n.º 1, enero de 2019, pp. 27-39, doi:10.15446/recolma.v53n1.81036.

Turabian

Hammou, Mustapha Ait, Elhoussine Azroul, y Badr Lahmi. «Topological degree methods for a Strongly nonlinear p(x)-elliptic problem». Revista Colombiana de Matemáticas 53, no. 1 (enero 1, 2019): 27–39. Accedido mayo 29, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/81036.

Vancouver

1.
Hammou MA, Azroul E, Lahmi B. Topological degree methods for a Strongly nonlinear p(x)-elliptic problem. rev.colomb.mat [Internet]. 1 de enero de 2019 [citado 29 de mayo de 2024];53(1):27-39. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/81036

Descargar cita

CrossRef Cited-by

CrossRef citations3

1. D. Nabab, J. Vélin. (2022). On a nonlinear elliptic system involving the (p(x),q(x))-Laplacian operator with gradient dependence. Complex Variables and Elliptic Equations, 67(7), p.1554. https://doi.org/10.1080/17476933.2021.1885385.

2. Adil Abbassi, Chakir Allalou, Abderrazak Kassidi. (2020). Topological degree methods for a Neumann problem governed by nonlinear elliptic equation. Moroccan Journal of Pure and Applied Analysis, 6(2), p.231. https://doi.org/10.2478/mjpaa-2020-0018.

3. Mustapha Ait Hammou, Elhoussine Azroul. (2021). Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent. Moroccan Journal of Pure and Applied Analysis, 7(1), p.50. https://doi.org/10.2478/mjpaa-2021-0006.

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