Nonradial large solutions of sublinear elliptic problems

El Mabrouk K, Hansen W (2007)
Journal of Mathematical Analysis and Applications 330(2): 1025-1041.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
El Mabrouk, Khalifa; Hansen, WolfhardUniBi
Abstract / Bemerkung
Let p be a nonnegative locally bounded function on R-N, N >= 3, and 0 < gamma < 1. Assuming that the oscillation sup(vertical bar x vertical bar=r) p(x) - inf(vertical bar x vertical bar=r) p(x) tends to zero as r -> infinity at a specified rate, it is shown that the equation Delta u = p(x)u(gamma) admits a positive solution in R-N satisfying lim(vertical bar x vertical bar ->infinity) u(x) = infinity if and only if integral(Rn) p(x)/vertical bar x vertical bar(N-2) dx = infinity. (c) 2006 Elsevier Inc. All rights reserved.
Stichworte
large solution; Greenian domain; Green; semilinear Dirichlet problem; function
Erscheinungsjahr
2007
Zeitschriftentitel
Journal of Mathematical Analysis and Applications
Band
330
Ausgabe
2
Seite(n)
1025-1041
ISSN
0022-247X
Page URI
https://pub.uni-bielefeld.de/record/1594788

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El Mabrouk K, Hansen W. Nonradial large solutions of sublinear elliptic problems. Journal of Mathematical Analysis and Applications. 2007;330(2):1025-1041.
El Mabrouk, K., & Hansen, W. (2007). Nonradial large solutions of sublinear elliptic problems. Journal of Mathematical Analysis and Applications, 330(2), 1025-1041. doi:10.1016/j.jmaa.2006.08.024
El Mabrouk, K., and Hansen, W. (2007). Nonradial large solutions of sublinear elliptic problems. Journal of Mathematical Analysis and Applications 330, 1025-1041.
El Mabrouk, K., & Hansen, W., 2007. Nonradial large solutions of sublinear elliptic problems. Journal of Mathematical Analysis and Applications, 330(2), p 1025-1041.
K. El Mabrouk and W. Hansen, “Nonradial large solutions of sublinear elliptic problems”, Journal of Mathematical Analysis and Applications, vol. 330, 2007, pp. 1025-1041.
El Mabrouk, K., Hansen, W.: Nonradial large solutions of sublinear elliptic problems. Journal of Mathematical Analysis and Applications. 330, 1025-1041 (2007).
El Mabrouk, Khalifa, and Hansen, Wolfhard. “Nonradial large solutions of sublinear elliptic problems”. Journal of Mathematical Analysis and Applications 330.2 (2007): 1025-1041.