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Abstract:

In this paper we consider singular quasilinear elliptic equations with quadratic gradient and a singular term with a variable exponent (Formula presented.) Here Ω is an open bounded set of RR, γ(x) is a positive continuous function and f is positive function that belongs to a certain Lebesgue space. We show, among other results, that there exists a solution in the natural energy space H0 1(Ω) to this problem when γ(x) is strictly less than 2 in a strip around the boundary; while there is no solution in the energy space when there exists(Formula presented.) with (Formula presented.) such that γ(x)>2 on Γ. Moreover, since we work by approximation we can analyze the behavior of the approximated solutions un in the case in which there is no solution in H0 1(Ω). © 2015, Springer Basel.

Registro:

Documento: Artículo
Título:A singular elliptic equation with natural growth in the gradient and a variable exponent
Autor:Carmona, J.; Martínez-Aparicio, P.J.; Rossi, J.D.
Filiación:Departamento de Matemáticas, Universidad de Almería, Ctra. Sacramento s/n, La Cañada de San Urbano, Almería, 04120, Spain
Departamento de Matemática Aplicada y Estadística, Campus Alfonso XIII, Universidad Politécnica de Cartagena, Murcia, 30203, Spain
Departamento de Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1, Buenos Aires, 1428, Argentina
Palabras clave:Nonlinear elliptic equations; Positive solutions; Singular natural growth gradient terms; Variable exponent
Año:2015
Volumen:22
Número:6
Página de inicio:1935
Página de fin:1948
DOI: http://dx.doi.org/10.1007/s00030-015-0351-0
Título revista:Nonlinear Differential Equations and Applications
Título revista abreviado:Nonlinear Diff. Equ. Appl.
ISSN:10219722
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v22_n6_p1935_Carmona

Referencias:

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Citas:

---------- APA ----------
Carmona, J., Martínez-Aparicio, P.J. & Rossi, J.D. (2015) . A singular elliptic equation with natural growth in the gradient and a variable exponent. Nonlinear Differential Equations and Applications, 22(6), 1935-1948.
http://dx.doi.org/10.1007/s00030-015-0351-0
---------- CHICAGO ----------
Carmona, J., Martínez-Aparicio, P.J., Rossi, J.D. "A singular elliptic equation with natural growth in the gradient and a variable exponent" . Nonlinear Differential Equations and Applications 22, no. 6 (2015) : 1935-1948.
http://dx.doi.org/10.1007/s00030-015-0351-0
---------- MLA ----------
Carmona, J., Martínez-Aparicio, P.J., Rossi, J.D. "A singular elliptic equation with natural growth in the gradient and a variable exponent" . Nonlinear Differential Equations and Applications, vol. 22, no. 6, 2015, pp. 1935-1948.
http://dx.doi.org/10.1007/s00030-015-0351-0
---------- VANCOUVER ----------
Carmona, J., Martínez-Aparicio, P.J., Rossi, J.D. A singular elliptic equation with natural growth in the gradient and a variable exponent. Nonlinear Diff. Equ. Appl. 2015;22(6):1935-1948.
http://dx.doi.org/10.1007/s00030-015-0351-0