The asymptotic behaviour of solutions with blow-up at the boundary for semilinear elliptic problems

Journal of Mathematical Analysis and Applications

Volumn 308, Issue 2, 2005, Pages 532-540

  Zhang, Zhijun ^a  

^a YANTAI UNIVERSITY   (China)

Author keywords

Large solutions; Precise asymptotic behaviour; Semilinear elliptic equations; Uniqueness

Indexed keywords

EID: 20744459155     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.11.029     Document Type: Article

References (23)

1. C. Bandle M. Marcus Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior J. Anal. Math. 58 1992 9-24
2. C. Bandle E. Giarrusso Boundary blowup for semilinear elliptic equations with nonlinear gradient terms Adv. Differential Equations 1 1996 133-150
3. F. Cirstea V.D. Radulescu Uniqueness of the blow-up boundary solution of logistic equations with absorption C. R. Acad. Sci. Paris Sér. I Math. 335 2002 447-452
4. F. Cirstea V.D. Radulescu Asymptotics for the blow-up boundary solution of the logistic equation with absorption C. R. Acad. Sci. Paris Sér. I Math. 336 2003 231-236
5. F. Cirstea V.D. Radulescu Solutions with boundary blow-up for a class of nonlinear elliptic problems Houston J. Math. 29 2003 821-829
6. G. Diaz R. Letelier Explosive solutions of quasilinear elliptic equation: Existence and uniqueness Nonlinear Anal. 20 1993 97-125
7. E. Giarrusso Asymptotic behavior of large solutions of an elliptic quasilinear equation with a borderline case C. R. Acad. Sci. Paris Sér. I Math. 331 2000 777-782
8. D. Gilbarg N.S. Trudinger Elliptic Partial Differential Equations of Second Order third ed. 1998 Springer-Verlag Berlin
9. A. Greco G. Porru Asymptotic estimates and convexity of large solutions to semilinear elliptic equations Differential Integral Equations 10 1997 219-229
10. J.B. Keller On solution of Δu=f(u) Comm. Pure Appl. Math. 10 1957 503-510
11. A.V. Lair A necessary and sufficient condition for existence of large solutions to semilinear elliptic equations J. Math. Anal. Appl. 240 1999 205-218
12. J.M. Lasry P.L. Lions Nonlinear elliptic equation with singular boundary conditions and stochastic control with state constraints Math. Z. 283 1989 583-630
13. A.C. Lazer P.J. McKenna On a problem of Bieberbach and Rademacher Nonlinear Anal. 21 1993 327-335
14. A.C. Lazer P.J. McKenna Asymptotic behavior of solutions of boundary blowup problems Differential Integral Equations 7 1994 1001-1019
15. C. Loewner L. Nirenberg Partial differential equations invariant under conformal or projective transformations in: Contributions to Analysis (a collection of papers dedicated to Lipman Bers) 1974 Academic Press New York 245-272
16. J. López-Gómez The boundary blow-up rate of large solutions J. Differential Equations 195 2003 25-45
17. M. Marcus L. Véron Uniqueness of solutions with blowup on the boundary for a class of nonlinear elliptic equations C. R. Acad. Sci. Paris Sér. I Math. 317 1993 557-563
18. V. Maric Regular Variation and Differential Equations Lecture Notes in Math. vol. 1726 2000 Springer-Verlag Berlin
19. R. Osserman On the inequality Δu ≥ f(u) Pacific J. Math. 7 1957 1641-1647
20. R. Seneta Regular Varying Functions Lecture Notes in Math. vol. 508 1976 Springer-Verlag Berlin
21. S. Tao Z. Zhang On the existence of explosive solutions for semilinear elliptic problems Nonlinear Anal. 48 2002 1043-1050
22. L. Véron Semilinear elliptic equations with uniform blowup on the boundary J. Anal. Math. 59 1992 231-250
23. Z. Zhang A remark on the existence of explosive solutions for a class of semilinear elliptic equations Nonlinear Anal. 41 2000 143-148