Positive solutions of an elliptic partial differential equation on RN

Journal of Mathematical Analysis and Applications

Volumn 271, Issue 2, 2002, Pages 409-425

  Du, Yihong ^a   Ma, Li ^b  

^a UNIVERSITY OF NEW ENGLAND   (Australia)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Boundary blow up; Comparison principle; Variational method

Indexed keywords

EID: 0037101516     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00124-5     Document Type: Article

References (20)

1. G.A. Afrouzi, K.J. Brown, On a diffusive logistic equation, J. Math. Anal. Appl. 225 (1998) 326-339.
2. P. Aviles, R. McOwen, Conformal deformation to constant negative scalar curvature on non-compact Riemannian manifolds, J. Differential Geom. 27 (1988) 225-239.
3. K.J. Brown, S.S. Lin, A. Tertikas, Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics, J. Math. Biol. 27 (1989) 91-104.
4. n, Indiana Univ. Math. J. 41 (1992) 261-278.
5. M.A. del Pino, Positive solutions of a semilinear elliptic equations on a compact manifold, Nonlinear Anal. 22 (1994) 1423-1430.
6. Y. Du, Q. Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal. 31 (1999) 1-18.
7. N by a squeezing method involving boundary blow-up solutions, J. London Math. Soc. 64 (2001) 107-124.
8. N, Comm. Partial Differential Equations 18 (1993) 215-240.
9. J.M. Fraile, P. Koch Medina, J. Lopez-Gomez, S. Merino, Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation, J. Differential Equations 127 (1996) 295-319.
10. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equation of Second Order, Springer-Verlag, 1977.
11. P. Hess, T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Partial Differential Equations 5 (1980) 999-1030.
12. Z.R. Jin, Principal eigenvalues with indefinite weight functions, Trans. Amer. Math. Soc. 349 (1997) 1945-1959.
13. J.L. Kazdan, F.W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J. Differential Geom. 10 (1985) 113-134.
14. p = 0 on complete Riemannian manifolds and their geometric applications, Trans. Amer. Math. Soc. 350 (1998) 1045-1078.
15. p = 0, Proc. Amer. Math. Soc. 95 (1985) 219-226.
16. L. Ma, Conformal deformations on a noncompact Riemannian manifold, Math. Ann. 295 (1993) 75-80.
17. M. Marcus, L. Veron, Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 237-274.
18. (n+2)/(n-2) = 0, its generalizations, and applications in geometry, Indiana Univ. Math. J. 31 (1982) 495-529.
19. p = 0 on the compact manifolds, Trans. Amer. Math. Soc. 331 (1992) 503-527.
20. n, Differential Integral Equations 8 (1995) 829-848.