Geodesic
Asymptotics for Semilinear Elliptic Systems
Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 514-519

Voir la notice de l'article provenant de la source Cambridge University Press

A class of weakly coupled systems of semilinear elliptic partial differential equations is considered in an exterior domain in RN, N > 3. Necessary and sufficient conditions are given for the existence of a positive solution (componentwise) with the asymptotic decay u(x) = O(|x|2-N ) as |x| —> ∞. Additional results concern the existence and structure of positive solutions u with finite energy in a neighbourhood of infinity.
DOI : 10.4153/CMB-1991-081-4
Mots-clés : 35J60, 35B05 
Noussair, Ezzat S.; Swanson, Charles A. Asymptotics for Semilinear Elliptic Systems. Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 514-519. doi: 10.4153/CMB-1991-081-4
@article{10_4153_CMB_1991_081_4,
     author = {Noussair, Ezzat S. and Swanson, Charles A.},
     title = {Asymptotics for {Semilinear} {Elliptic} {Systems}},
     journal = {Canadian mathematical bulletin},
     pages = {514--519},
     year = {1991},
     volume = {34},
     number = {4},
     doi = {10.4153/CMB-1991-081-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-081-4/}
}
TY  - JOUR
AU  - Noussair, Ezzat S.
AU  - Swanson, Charles A.
TI  - Asymptotics for Semilinear Elliptic Systems
JO  - Canadian mathematical bulletin
PY  - 1991
SP  - 514
EP  - 519
VL  - 34
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-081-4/
DO  - 10.4153/CMB-1991-081-4
ID  - 10_4153_CMB_1991_081_4
ER  - 
%0 Journal Article
%A Noussair, Ezzat S.
%A Swanson, Charles A.
%T Asymptotics for Semilinear Elliptic Systems
%J Canadian mathematical bulletin
%D 1991
%P 514-519
%V 34
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-081-4/
%R 10.4153/CMB-1991-081-4
%F 10_4153_CMB_1991_081_4

[1] 1. Brezis, H. and Kato, T., Remarks on the Schrodinger operator with singular complex potential, J. Math Pures App. 58 (1979), 137–151. Google Scholar

[2] 2. Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order. 2nd éd., Springer- Verlag, Berlin-Heidelberg-New York-Tokyo, 1983. Google Scholar

[3] 3. Kawano, N., On bounded entire solutions of semilinear elliptic equations, Hiroshima Math. J. 14 (1984), 125–158. Google Scholar

[4] 4. Kawano, N. and Kusano, T., On positive entire solutions of a class of second order semilinear elliptic systems, Math. Z. 186 (1984), 287–297. Google Scholar

[5] 5. Miranda, C., Partial differential equations of elliptic type. Springer- Verlag, New York-Heidelberg-Berlin, 1970. Google Scholar

[6] 6. Noussair, E. S. and Swanson, C. A., Oscillation theory for semilinear Schrodingerequations and inequalities, Proc. Roy. Soc. Edinburgh A75( 1975/76), 67–81. Google Scholar

[7] 7. Noussair, E. S. and Swanson, C. A., Global positive solutions of semilinear elliptic equations, Canad. J. Math. 35 (1983), 839–861. Google Scholar

[8] 8. Serrin, J., Isolated singularities of solutions of quasi-linear equations, Acta Math. 113 (1965), 219–240. Google Scholar

[9] 9. Swanson, C. A., Extremal positive solutions of semilinear Schrodinger equations, Canad. Math Bull. 26 (1983), 171-178. Google Scholar

[10] 10. Swanson, C. A., Positive solutions of -Δu =f(x,u), Nonlinear Anal. 9 (1985), 1319–1323. Google Scholar

Cité par Sources :