A Necessary and Sufficient Condition for Existence of Large Solutions to Semilinear Elliptic Equations

Journal of Mathematical Analysis and Applications

Volumn 240, Issue 1, 1999, Pages 205-218

  Lair, Alan V ^a  

^a AIR FORCE INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Elliptic equation; Large solution; Semilinear equation

Indexed keywords

EID: 0004361518     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6609     Document Type: Article

References (14)

1. Bandle C., Marcus M. "Large" solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior. J. Analyse Math. 58:1992;9-24.
2. Bers L., John F., Schechter M. Partial Differential Equations. Lectures in Applied Mathematics. 3:1971;Am. Math. Soc. Providence.
3. 2u. Trans. Amer. Math. Soc. 304:1987;639-668.
4. N. Indiana Univ. Math. J. 41:1992;261-278.
5. Gilbarg D., Trudinger N. S. Elliptic Partial Differential Equations of Second Order. 1977;Springer-Verlag, Berlin/Heidelberg/New York.
6. Keller J. B. On solution of Δu = f(u). Comm. Pure Appl. Math. 10:1957;503-510.
7. Ladyzhenskaya O. A., Ural'tseva N. N. Linear and Quasilinear Elliptic Equations. 1968;Academic Press, New York/London.
8. Lair A. V., Shaker A. W. Classical and weak solutions of a singular semilinear elliptic problem. J. Math. Anal. Appl. 211:1997;371-385.
9. Lair A. V., Wood A. W. Large solutions of semilinear elliptic problems. Nonlinear Anal. 37:1999;805-812.
10. Lazer A. C., McKenna P. J. On a problem of Bieberbach and Rademacher. Nonlinear Anal. 21:1993;327-335.
11. Marcus M. On solutions with blow-up at the boundary for a class of semilinear elliptic equations. Buttazzo G., Galdi G., Zanghirati L. Developments in Partial Differential Equations and Applications to Mathematical Physics. 1992;65-77 Plenum, New York.
12. Osserman R. On the inequality Δu ≥ f(u). Pacific J. Math. 7:1957;1641-1647.
13. 2. Soviet Math. Dokl. 1:1961;1143-1146.
14. Sattinger D. Topics in Stability and Bifurcation Theory. 1973;Springer-Verlag, Berlin/Heidelberg/New York.