Geodesic
Asymptotic Theory of Singular Semilinear Elliptic Equations
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 223-232

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

Necessary and sufficient conditions are found for the existence of two positive solutions of the semilinear elliptic equation Δu + q(|x|)u = f(x, u) in an exterior domain Ω⊂Rn, n ≥ 1, where q, f are real-valued and locally Hölder continuous, and f(x, u) is nonincreasing in u for each fixed x∈Ω. An example is the singular stationary Klein-Gordon equation Δu — k 2 u = p(x)u -λ where k and λ are positive constants. In this case NASC are given for the existence of two positive solutions u i (x) in some exterior subdomain of Ω such that both |x|m exp[(-l)i-1 k|x|]u i (x) are bounded and bounded away from zero in this subdomain, m = (n —1)/2, i = 1, 2.
DOI : 10.4153/CMB-1984-032-1
Mots-clés : 35B05, 35J60, 34C11, 34EXX 
Kusano, Takaŝi; Swanson, Charles A. Asymptotic Theory of Singular Semilinear Elliptic Equations. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 223-232. doi: 10.4153/CMB-1984-032-1
@article{10_4153_CMB_1984_032_1,
     author = {Kusano, Taka\^{s}i and Swanson, Charles A.},
     title = {Asymptotic {Theory} of {Singular} {Semilinear} {Elliptic} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {223--232},
     year = {1984},
     volume = {27},
     number = {2},
     doi = {10.4153/CMB-1984-032-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-032-1/}
}
TY  - JOUR
AU  - Kusano, Takaŝi
AU  - Swanson, Charles A.
TI  - Asymptotic Theory of Singular Semilinear Elliptic Equations
JO  - Canadian mathematical bulletin
PY  - 1984
SP  - 223
EP  - 232
VL  - 27
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-032-1/
DO  - 10.4153/CMB-1984-032-1
ID  - 10_4153_CMB_1984_032_1
ER  - 
%0 Journal Article
%A Kusano, Takaŝi
%A Swanson, Charles A.
%T Asymptotic Theory of Singular Semilinear Elliptic Equations
%J Canadian mathematical bulletin
%D 1984
%P 223-232
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-032-1/
%R 10.4153/CMB-1984-032-1
%F 10_4153_CMB_1984_032_1

[1] 1. Callegari, A. J. and Nachman, A., Some singular, nonlinear differential equations arising in boundary layer theory, J. Math. Anal. Appl. 64 (1978), 96–105. Google Scholar

[2] 2. Callegari, A. J. and Nachman, A., A nonlinear singular boundary value problem in the theory of pseudoplastic fluids, SIAM J. Appl. Math. 38 (1980), 275–281. Google Scholar

[3] 3. Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G., and Staff, Bateman Project, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York-Toronto-London, 1953. Google Scholar

[4] 4. Kitamura, Yuichi and Kusano, Takasi, Nonlinear oscillations of higher-order functional differential equations with deviating arguments, J. Math. Anal. Appl. 77 (1980), 100–119. Google Scholar

[5] 5. Kreith, Kurt and Swanson, C. A., Asymptotic solutions of semilinear elliptic equations, J. Math. Anal. Appl., 98 (1984). Google Scholar

[6] 6. Ladyzhenskaya, O. A. and Ural’tseva, N. N., Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Google Scholar

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

[8] 8. Noussair, E. S. and Swanson, C. A., Positive solutions of quasilinear elliptic equations in exterior domains, J. Math. Anal. Appl. 75 (1980), 121–133. Google Scholar

[9] 9. Taliaferro, Steven, On the positive solutions of y"+ ϕ(t)y-λ = 0, Nonlinear Anal. 2 (1978) 437–466. Google Scholar

[10] 10. Taliaferro, Steven, Asymptotic behavior of solutions of y" = ϕ(t)yλ J-Math. Anal. Appl. 66 (1978), 95–134. Google Scholar

[11] 11. Trench, W. F., Canonical forms and principal systems for general disconjugate equations, Trans. Amer. Math. Soc. 189 (1974), 319–327. Google Scholar

Cité par Sources :