Solutions of some nonlinear elliptic problems, which are singular on a submanifold

Journal des Mathematiques Pures et Appliquees

Volumn 76, Issue 9, 1997, Pages 757-776

  Grillot, Michèle ^a  

^a UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031280884     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(97)89968-0     Document Type: Article

References (21)

1. [1] C. BANDLE and M. MARCUS, Large solutions of semilinear elliptic equations : existence, uniqueness and asymptotic behaviour, Jl. Analyse Math., 58, 1992, pp. 9-24.
2. [2] P. BARAS et M. PIERRE, Singularités éliminables pour des équations semi-linéaires, Ann. Inst. Fourier, 34, 1984, pp. 185-206.
3. [3] M. BERGER, P. GAUDUCHON and E. MAZET, Le spectre d'une variété Riemannienne, Springer-Verlag, 1971.
4. [4] H. BREZIS and L. VERON. Removable singularities of some nonlinear elliptic equations, Arch. Rational Mech. Anal., 75, 1980, pp. 1-6.
5. N, Jl. Funct. Anal., 83, 1989, pp. 50-98.
6. [6] E. B. DYNKIN, A probabilistic approach to one class of nonlinear differential equations, Prob. Th. Rel. Fields, 89, 1991, pp. 89-115.
7. [7] R. EMDEN, Gaskugeln, Anwendungen der mechanischen Warmertheorie auf Kosmologie und meteorologische Problem. XII, Teubner - Leibzig, 1897.
8. [8] R.H. FOWLER, Further studies on Emden's and similar differential equations, Quart. J. Math., 2, 1931, pp. 259-288.
9. [9] A. GRAY, TUBES, Addison-Wesley publishing company, 1990.
10. [10] M. GRILLOT, Solutions singulières sur une sous-variété d'équations elliptiques non linéaires, C. R. Acad. Sci., 322, 1996, pp. 49-54.
11. [11] J.B. KELLER, On solutions of Δu = f(u), Comm. Appl. Math., 10, 1957, pp. 503-510.
12. st European Congress of Mathematics, 2, pp. 185-212, Birkhauser, Boston.
13. [13] C. LOEWNER and L. NIRENBERG, Partial differential equations invariant under conformal or projective transformations, Contributions to Analysis, Academic Press, New York, 1974, pp. 245-272.
14. [14] M. MARCUS and L. VERON, Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. I.H.P. Anal. non Lin., 14, 1997, pp. 237-274.
15. [15] S. OSSERMAN, On the inequality Δu ≥ f(u), Pacific Jl. Math. 7, 1957, pp. 1641-1647.
16. [16] A. RATTO, M. RIGOLI and L. VERON, Scalar curvature and conformal deformations of hyperbolic space, Jl. Funct. Analysis, 121, 1994, pp. 15-77.
17. [17] J. L. VAZQUEZ and L. VERON, Singularities of elliptic equations with an exponential non linearity, Math. Ann., 269, 1984, pp. 119-135.
18. [18] L. VERON, Singularités éliminables d'équations elliptiques non linéaires, Jl. Differential Equations, 41, 1981, pp. 87-95.
19. [19] L. VERON, Singular solutions of some nonlinear equations, Nonlinear Anal., 5, 1981, pp. 225-242.
20. [20] L. VERON, Weak and strong singularities of nonlinear elliptic equations, Proceed. Sympo. Pure Math., 45, part 2, 1986, pp. 477-495.
21. [21] L. VERON, Semilinear elliptic equations with uniform blowup on the boundary, J. Anal. Math., 59, 1992, pp. 231-250.