Large Solutions for the Laplacian With a Power Nonlinearity Given by a Variable Exponent

GarcíA-MeliáN, Jorge; Rossi, Julio D.; Sabina De Lis, José C.

doi:10.1016/j.anihpc.2008.03.007

GarcíA-MeliáN, Jorge ; Rossi, Julio D. ; Sabina De Lis, José C.

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 3, pp. 889-902

MR Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2008.03.007

@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},
     year = {2009},
     publisher = {Elsevier},
     volume = {26},
     number = {3},
     doi = {10.1016/j.anihpc.2008.03.007},
     mrnumber = {2526407},
     zbl = {1177.35072},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2008.03.007/}
}

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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

Bibliographie
Cité par

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

[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. | Zbl | MR

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

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

[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. | Zbl | MR

[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. | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR

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

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

[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. | Zbl | MR

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

[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. | Zbl | MR

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

[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. | Zbl | MR

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

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

[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. | Zbl | MR | Numdam

[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. | Zbl | MR

[25] Osserman R., On the Inequality $Δ u \geq f (u)$ , Pacific J. Math. 7 (1957) 1641-1647. | Zbl | MR

[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. | Zbl | MR

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

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