@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://www.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://www.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://www.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://www.numdam.org/articles/10.1016/j.anihpc.2008.03.007/
[1] On the Existence of Positive Solutions of Nonlinear Elliptic Boundary Value Problems, Indiana Univ. Math. J. 21 (1971/72) 125-146. | MR | Zbl
,[2] 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] ‘Large' Solutions of Semilinear Elliptic Equations: Existence, Uniqueness and Asymptotic Behaviour, J. Anal. Math. 58 (1992) 9-24. | MR | Zbl
, ,[4] Und Die Automorphen Funktionen, Math. Ann. 77 (1916) 173-212. | EuDML | MR
,[5] 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] Uniqueness and Boundary Behaviour of Large Solutions to Elliptic Problems With Singular Weights, Comm. Pure Appl. Anal. 3 (2004) 653-662. | MR | Zbl
, , , ,[7] The Influence of Domain Geometry in Boundary Blow-Up Elliptic Problems, Nonlinear Anal. 48 (6) (2002) 897-904. | MR | Zbl
, ,[8] 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] Combining Linear and Nonlinear Diffusion, Adv. Nonlinear Stud. 4 (2004) 273-287. | MR | Zbl
, , ,[10] Singular Boundary Value Problems of a Porous Media Logistic Equation, Hiroshima Math. J. 34 (2004) 57-80. | MR | Zbl
, , ,[11] Explosive Solutions of Quasilinear Elliptic Equations: Existence and Uniqueness, Nonlinear Anal. 20 (1993) 97-125. | MR | Zbl
, ,[12] Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations, SIAM J. Math. Anal. 31 (1999) 1-18. | MR | Zbl
, ,[13] Back to the Keller-Osserman Condition for Boundary Blow-Up Solutions, Adv. Nonlinear Stud. 7 (2007) 271-298. | MR | Zbl
, , , ,[14] Nondegeneracy and Uniqueness for Boundary Blow-Up Elliptic Problems, J. Differential Equations 223 (2006) 208-227. | MR | Zbl
,[15] Uniqueness for Boundary Blow-Up Problems With Continuous Weights, Proc. Amer. Math. Soc. 135 (2007) 2785-2793. | MR | Zbl
,[16] 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] On Solutions of , Comm. Pure Appl. Math. 10 (1957) 503-510. | MR | Zbl
,[18] 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] Large Solutions of Sublinear Elliptic Equations, Nonlinear Anal. 39 (2000) 745-753. | MR | Zbl
, ,[20] 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] Varying Stoichometric Exponents I: Classical Steady States and Metasolutions, Adv. Nonlinear Stud. 3 (2003) 327-354. | MR | Zbl
,[22] Combining Fast, Linear and Slow Diffusion, Topol. Methods Nonlinear Anal. 23 (2004) 275-300. | MR | Zbl
, ,[23] 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] Large Solutions to Some Non-Linear O.D.E. With Singular Coefficients, Nonlinear Anal. 47 (2001) 513-524. | MR | Zbl
, , ,[25] On the Inequality , Pacific J. Math. 7 (1957) 1641-1647. | MR | Zbl
,[26] 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] Semilinear Elliptic Equations With Uniform Blowup on the Boundary, J. Anal. Math. 59 (1992) 231-250. | MR | Zbl
,[28] A Remark on the Existence of Explosive Solutions for a Class of Semilinear Elliptic Equations, Nonlinear Anal. 41 (2000) 143-148. | MR | Zbl
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