On positive entire solutions to a class of equations with a singular coefficient and critical exponent

Advances in Differential Equations

Volumn 1, Issue 2, 1996, Pages 241-264

  Terracini, Susanna ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000155087     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. A. Bahri and J.M. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., 41 (1988), 253-294.
2. N, Rev. Mat. Iberoamericana., 6 (1990), 1-15.
3. H. Berestycki and P.L. Lions, Nonlinear scalar fields equations I, existence of a ground state, Arch. Rat. Mech. Anal., 82 (1983), 313-375.
4. H. Brezis, Nonlinear Elliptic equations involving the critical Sobolev exponent - Survey and perspectives, in "Direction in Partial Differential Equations," Ed. by Crandall et al. (1987), 17-36.
5. H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., 88 (1983), 486-490.
6. H. Brezis and L. Nirenberg, Positive solutions of Nonlinear elliptic equations involving Critical exponents, Comm. Pure Appl. Math., 36 (1983), 437-477.
7. L. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behaviour of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math., 42 (1989) 271-297.
8. H. Egnell, Elliptic boundary value problems with singular coefficients and critical nonlinearity, Indiana Univ. Math. J., 38 (1989), 235-251.
9. B. Gidas, W.M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243.
10. n, Math. Anal. and Applic., Part A, Advances in Math. Suppl. Studies 7A, ed. L. Nachbin, Academic Press (1981), 209-243.
11. D. Joseph and T. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal., 49 (1973), 241-269.
12. Congming Li, Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains, Comm. Partial Differential Equations., 16 (1991), 585-615.
13. S.I. Pohozaev, Eigenfunctions of the equation Δu +λf(u) Sov. Math. Doklady., 5 (1965), 1408-1411.
14. M. Reed and B. Simon, "Methods of Modern Mathematical Physics," vol. I, II, Academic Press, New York (1975).
15. J. Serrin, A symmetry problem in potential theory, Arch. Rat. Mech., 43 (1971), 304-318.
16. M. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z., 187 (1984), 511-517.
17. M. Struwe, "Variational Methods and Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems," Springer-Verlag, Berlin/New York (1990).
18. G. Talenti, Best constants in Sobolev inequality, Annali di Mat., 110 (1976), 353-372.
19. S. Terracini, Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions, To appear in Differential and Integral Equations.