Geodesic
Radial Entire Solutions of Even Order Semilinear Elliptic Equations
Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1281-1300

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

Semilinear elliptic partial differential equations of the type 1 will be considered throughout real Euclidean N-space, where m ≧ 2 is a positive integer, Δ denotes the N-dimensional Laplacian, and f is a real-valued continuous function in [0, ∞) × (0, ∞). Detailed hypotheses on the structure of f are listed in Section 3.Our objective is to prove the existence of radially symmetric positive entire solutions u(x) of (1) which are asymptotic to positive constant multiples of |x|2m−2i as |x| → ∞ for every i = 1,..., m, N ≧ 2i + 1. 
Kusano, Takaŝi; Naito, Manabu; Swanson, Charles A. Radial Entire Solutions of Even Order Semilinear Elliptic Equations. Canadian journal of mathematics, Tome 40 (1988) no. 6, pp. 1281-1300. doi: 10.4153/CJM-1988-056-3
@article{10_4153_CJM_1988_056_3,
     author = {Kusano, Taka\^{s}i and Naito, Manabu and Swanson, Charles A.},
     title = {Radial {Entire} {Solutions} of {Even} {Order} {Semilinear} {Elliptic} {Equations}},
     journal = {Canadian journal of mathematics},
     pages = {1281--1300},
     year = {1988},
     volume = {40},
     number = {6},
     doi = {10.4153/CJM-1988-056-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-056-3/}
}
TY  - JOUR
AU  - Kusano, Takaŝi
AU  - Naito, Manabu
AU  - Swanson, Charles A.
TI  - Radial Entire Solutions of Even Order Semilinear Elliptic Equations
JO  - Canadian journal of mathematics
PY  - 1988
SP  - 1281
EP  - 1300
VL  - 40
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-056-3/
DO  - 10.4153/CJM-1988-056-3
ID  - 10_4153_CJM_1988_056_3
ER  - 
%0 Journal Article
%A Kusano, Takaŝi
%A Naito, Manabu
%A Swanson, Charles A.
%T Radial Entire Solutions of Even Order Semilinear Elliptic Equations
%J Canadian journal of mathematics
%D 1988
%P 1281-1300
%V 40
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-056-3/
%R 10.4153/CJM-1988-056-3
%F 10_4153_CJM_1988_056_3

[1] 1. Fink, A. M. and Kusano, T., Nonoscillation theorems for differential equations with general deviating arguments, Lecture Notes in Mathematics 1032 (Springer, 1983), 224–239. Google Scholar

[2] 2. Fukagai, N., On decaying entire solutions of second order sublinear elliptic equations, Hiroshima Math. J. 14 (1984), 551–562. 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. Kusano, T., Naito, M. and Swanson, C. A., Radial entire solutions to even order semilinear elliptic equations in the plane, Proc. Roy. Soc. Edinburgh Sect. A 105 (1987), 275–287. Google Scholar

[5] 5. Kusano, T. and Oharu, S., Bounded entire solutions of second order semilinear elliptic equations with application to a parabolic initial value problem, Indiana Univ. Math J. 34 (1985) 85–95. Google Scholar

[6] 6. Kusano, T. and Swanson, C. A., Positive entire solutions of semilinear biharmonic equations, Hiroshima Math. J. 17 (1987), 13–28. Google Scholar

[7] 7. Kusano, T. and Trench, W. F., Global existence of solutions of mixed sublinear-sup erlinear differential equations, Hiroshima Math. J. 16 (1986), 597–606. Google Scholar

[8] 8. Walter, W., Game Lösungen der Differentialgleichung Δpu = f(u), Math. Z. 67 (1957), 32–37. Google Scholar

[9] 9. Walter, W., Zur Existenz gamer Lö;sungen der Differentialgleichung Δpu = eu , Arch. Math. 9 (1958), 308–312. Google Scholar

[10] 10. Walter, W. and Rhee, H., Entire solutions of Δpu = f(r,u), Proc. Roy. Soc Edinburgh Sect. A 82 (1979), 189–192. Google Scholar

Cité par Sources :