Large Solutions for the Laplacian With a Power Nonlinearity Given by a Variable Exponent
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 3, pp. 889-902.
@article{AIHPC_2009__26_3_889_0,
     author = {Garc{\'\i}A-Meli\'aN, Jorge and Rossi, Julio D. and Sabina De Lis, Jos\'e C.},
     title = {Large {Solutions} for the {Laplacian} {With} a {Power} {Nonlinearity} {Given} by a {Variable} {Exponent}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {889--902},
     publisher = {Elsevier},
     volume = {26},
     number = {3},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.03.007},
     mrnumber = {2526407},
     zbl = {1177.35072},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.007/}
}
TY  - JOUR
AU  - GarcíA-MeliáN, Jorge
AU  - Rossi, Julio D.
AU  - Sabina De Lis, José C.
TI  - Large Solutions for the Laplacian With a Power Nonlinearity Given by a Variable Exponent
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 889
EP  - 902
VL  - 26
IS  - 3
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.007/
DO  - 10.1016/j.anihpc.2008.03.007
LA  - en
ID  - AIHPC_2009__26_3_889_0
ER  - 
%0 Journal Article
%A GarcíA-MeliáN, Jorge
%A Rossi, Julio D.
%A Sabina De Lis, José C.
%T Large Solutions for the Laplacian With a Power Nonlinearity Given by a Variable Exponent
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 889-902
%V 26
%N 3
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.007/
%R 10.1016/j.anihpc.2008.03.007
%G en
%F AIHPC_2009__26_3_889_0
GarcíA-MeliáN, Jorge; Rossi, Julio D.; Sabina De Lis, José C. Large Solutions for the Laplacian With a Power Nonlinearity Given by a Variable Exponent. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 3, pp. 889-902. doi : 10.1016/j.anihpc.2008.03.007. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.03.007/

[1] Amann H., On the Existence of Positive Solutions of Nonlinear Elliptic Boundary Value Problems, Indiana Univ. Math. J. 21 (1971/72) 125-146. | MR | Zbl

[2] Bandle C., Marcus M., Sur Les Solutions Maximales De Problèmes Elliptiques Non Linéaires : Bornes Isopérimetriques Et Comportement Asymptotique, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990) 91-93. | MR | Zbl

[3] Bandle C., Marcus M., ‘Large' Solutions of Semilinear Elliptic Equations: Existence, Uniqueness and Asymptotic Behaviour, J. Anal. Math. 58 (1992) 9-24. | MR | Zbl

[4] Bieberbach L., Δu=e u Und Die Automorphen Funktionen, Math. Ann. 77 (1916) 173-212. | EuDML | MR

[5] Chuaqui M., Cortázar C., Elgueta M., Flores C., García-Melián J., Letelier R., On an Elliptic Problem With Boundary Blow-Up and a Singular Weight: the Radial Case, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 1283-1297. | MR | Zbl

[6] Chuaqui M., Cortázar C., Elgueta M., García-Melián J., Uniqueness and Boundary Behaviour of Large Solutions to Elliptic Problems With Singular Weights, Comm. Pure Appl. Anal. 3 (2004) 653-662. | MR | Zbl

[7] Del Pino M., Letelier R., The Influence of Domain Geometry in Boundary Blow-Up Elliptic Problems, Nonlinear Anal. 48 (6) (2002) 897-904. | MR | Zbl

[8] Delgado M., Lopez-Gomez J., Suárez A., Characterizing the Existence of Large Solutions for a Class of Sublinear Problems With Nonlinear Diffusion, Adv. Differential Equations 7 (2002) 1235-1256. | MR | Zbl

[9] Delgado M., Lopez-Gomez J., Suárez A., Combining Linear and Nonlinear Diffusion, Adv. Nonlinear Stud. 4 (2004) 273-287. | MR | Zbl

[10] Delgado M., Lopez-Gomez J., Suárez A., Singular Boundary Value Problems of a Porous Media Logistic Equation, Hiroshima Math. J. 34 (2004) 57-80. | MR | Zbl

[11] Díaz G., Letelier R., Explosive Solutions of Quasilinear Elliptic Equations: Existence and Uniqueness, Nonlinear Anal. 20 (1993) 97-125. | MR | Zbl

[12] Du Y., Huang Q., Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations, SIAM J. Math. Anal. 31 (1999) 1-18. | MR | Zbl

[13] Dumont S., Dupaigne L., Goubet O., Rădulescu V., Back to the Keller-Osserman Condition for Boundary Blow-Up Solutions, Adv. Nonlinear Stud. 7 (2007) 271-298. | MR | Zbl

[14] García-Melián J., Nondegeneracy and Uniqueness for Boundary Blow-Up Elliptic Problems, J. Differential Equations 223 (2006) 208-227. | MR | Zbl

[15] García-Melián J., Uniqueness for Boundary Blow-Up Problems With Continuous Weights, Proc. Amer. Math. Soc. 135 (2007) 2785-2793. | MR | Zbl

[16] García-Melián J., Letelier-Albornoz R., Sabina De Lis J., Uniqueness and Asymptotic Behaviour for Solutions of Semilinear Problems With Boundary Blow-Up, Proc. Amer. Math. Soc. 129 (12) (2001) 3593-3602. | MR | Zbl

[17] Keller J. B., On Solutions of Δu=fu, Comm. Pure Appl. Math. 10 (1957) 503-510. | MR | Zbl

[18] Kondrat'Ev V. A., Nikishkin V. A., Asymptotics, Near the Boundary, of a Solution of a Singular Boundary Value Problem for a Semilinear Elliptic Equation, Differential Equations 26 (1990) 345-348. | MR | Zbl

[19] Lair A., Wood A. W., Large Solutions of Sublinear Elliptic Equations, Nonlinear Anal. 39 (2000) 745-753. | MR | Zbl

[20] Loewner C., Nirenberg L., Partial Differential Equations Invariant Under Conformal of Projective Transformations, in: Contributions to Analysis (a Collection of Papers Dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 245-272. | MR | Zbl

[21] Lopez-Gomez J., Varying Stoichometric Exponents I: Classical Steady States and Metasolutions, Adv. Nonlinear Stud. 3 (2003) 327-354. | MR | Zbl

[22] Lopez-Gomez J., Suárez A., Combining Fast, Linear and Slow Diffusion, Topol. Methods Nonlinear Anal. 23 (2004) 275-300. | MR | Zbl

[23] Marcus M., Véron L., Uniqueness and Asymptotic Behaviour of Solutions With Boundary Blow-Up for a Class of Nonlinear Elliptic Equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (2) (1997) 237-274. | Numdam | MR | Zbl

[24] Mohammed M., Porcu G., Porru G., Large Solutions to Some Non-Linear O.D.E. With Singular Coefficients, Nonlinear Anal. 47 (2001) 513-524. | MR | Zbl

[25] Osserman R., On the Inequality Δufu, Pacific J. Math. 7 (1957) 1641-1647. | MR | Zbl

[26] Rădulescu V., Singular Phenomena in Nonlinear Elliptic Problems: From Boundary Blow-Up Solutions to Equations With Singular Nonlinearities, in: Handbook of Differential Equations: Stationary Partial Differential Equations, vol. 4, 2007, pp. 483-591.

[27] Véron L., Semilinear Elliptic Equations With Uniform Blowup on the Boundary, J. Anal. Math. 59 (1992) 231-250. | MR | Zbl

[28] Zhang Z., A Remark on the Existence of Explosive Solutions for a Class of Semilinear Elliptic Equations, Nonlinear Anal. 41 (2000) 143-148. | MR | Zbl

Cité par Sources :