Uniqueness of large solutions

Journal of Mathematical Analysis and Applications

Volumn 395, Issue 2, 2012, Pages 806-812

  Costin, O ^a   Dupaigne, L ^b   Goubet, O ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Boundary blow up; Elliptic partial differential equations; Large solutions

Indexed keywords

EID: 84864000180     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2012.05.085     Document Type: Article

References (15)

1. Keller J.B. On solutions of δu=f(u). Comm. Pure Appl. Math. 1957, 10:503-510. MR0091407 (19,964c).
2. Osserman Robert On the inequality δu≥f(u). Pacific J. Math. 1957, 7:1641-1647. MR0098239 (20 #4701).
3. Dumont Serge, Dupaigne Louis, Goubet Olivier, Rǎdulescu Vicentiu Back to the Keller-Osserman condition for boundary blow-up solutions. Adv. Nonlinear Stud. 2007, 7(2):271-298. MR2308040 (2008e:35062).
4. Véron Laurent Generalized boundary value problems for nonlinear elliptic equations. Electron. J. Differ. Equ. Conf. 2001, vol. 6:313-342. Southwest Texas State Univ., San Marcos, TX, (electronic). MR1804784 (2001j:35099).
5. Costin O., Dupaigne L. Boundary blow-up solutions in the unit ball: asymptotics, uniqueness and symmetry. J. Differential Equations 2010, 249(4):931-964. MR2652158 (2011e:35125). 10.1016/j.jde.2010.02.023.
6. Reichel W., Walter W. Radial solutions of equations and inequalities involving the p-Laplacian. J. Inequal. Appl. 1997, 1(1):47-71.
7. Marcus Moshe, Véron Laurent Existence and uniqueness results for large solutions of general nonlinear elliptic equations. J. Evol. Equ. 2003, 3(4):637-652. Dedicated to Philippe Bénilan. MR2058055 (2005c:35103). 10.1007/s00028-003-0122-y.
8. García-Melián Jorge Uniqueness of positive solutions for a boundary a blow-up problem. J. Math. Anal. Appl. 2009, 360(2):530-536. MR2561251 (2011a:35174). 10.1016/j.jmaa.2009.06.077.
9. Bandle Catherine, Marcus Moshe Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behaviour. J. Anal. Math. 1992, 58:9-24. Festschrift on the occasion of the 70th birthday of Shmuel Agmon. MR1226934 (94c:35081). 10.1007/BF02790355.
10. Payne L.E., Stakgold Ivar Nonlinear problems in nuclear reactor analysis. Lecture Notes in Mathematics 1973, vol. 322. Springer-Verlag, Berlin, MR0371548 (51 #7766).
11. Sperb Renè P. Maximum Principles and their Applications. Mathematics in Science and Engineering 1981, vol. 157. Academic Press Inc., Harcourt Brace Jovanovich Publishers, New York, MR615561 (84a:35033).
12. n. Manuscripta Math. 1992, 74(1):87-106. MR1141779 (93f:35062). 10.1007/BF02567660.
13. Laurent Véron, Personal communication.
14. Montenegro Marcelo, Ponce Augusto C. The sub-supersolution method for weak solutions. Proc. Amer. Math. Soc. 2008, 136(7):2429-2438. MR2390510 (2010h:35160). 10.1090/S0002-9939-08-09231-9.
15. Véron Laurent Solutions singulières d'équations elliptiques semilinéaires. C. R. Acad. Sci. Paris Sér. A-B 1979, 288(18):A867-A869. (in French, with English summary). MR538992 (80h:35038).