Asymptotic estimates and qualitative properties of an elliptic problem in dimension two

Advanced Nonlinear Studies

Volumn 4, Issue 1, 2004, Pages 15-36

  El Mehdi, Khalil ^a   Grossi, Massimo ^b  

^a University of Nouakchott El Asriya   (Mauritania)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Least energy solution; Semilinear elliptic equations

Indexed keywords

EID: 3042844222     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2004-0102     Document Type: Article

References (18)

1. N, and related topics, J. Funct. Anal. 165 (1999), 117-149.
2. G. Blanchi and H. Egnell, A note on the Sobolev inequality, J. Funct. Anal. 100 (1991), 18-24.
3. u in two dimension, Comm. Part. Diff. Eqns. 16 (1991), 1223-1253.
4. X. Cabré and S. Chanillo, Stable solutions of semilinear elliptic problems in convex domains, Selecta Math. (N.S.) 4 (1998), 1-10.
5. W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), 615-622.
6. E.N. Dancer, On the uniqueness of the positive solution of a singularly perturbed problem, Rocky Mount. J. Math. 25 1995, 957-975.
7. D.G. de Figueiredo, P.L. Lions and R.D. Nussbaum, A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pures Appl. 61 (1982), 41-63.
8. H. Federer, Geometric measure theory, Spinger-Verlag, 1969.
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. B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Par. Diff. Eqns. 6 (1981), 883-901.
11. D. Gilbarg and N. Trudinger, Elliptic partial differential equation of second order, Second edition, Springer Verlag, 1983.
12. M. Grossi and R. Molle, On the shape of the solutions of some semilinear elliptic problems, Commun. Contemp. Math. 5 (2003), 85-99.
13. 2, Manuscripta Math. 84 (1994), 13-19.
14. L.E. Payne, On two conjectures in the fixed membrane eigenvalue problem, Z. Angew. Math. Phys. 24 (1973), 721-729.
15. O. Rey The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990), 1-52.
16. X. Ren and J. Wei, On a two-dimensional elliptic problem with large exponent in nonlinearity, Trans. A.M.S. 343(1994), 749-763.
17. X. Ren and J. Wei, Asymptotic Symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Proc. A.M.S. 42 (1989), 271-297.
18. R. Sperb, Extension of two theorems of Payne to some nonlinear Dirichlet problems, Z. Angew. Math. Phys. 26 (1975), 721-726.