Second-order semilinear elliptic inequalities in exterior domains

Kondratiev Y, Liskevich V, Sobol Z (2003)
JOURNAL OF DIFFERENTIAL EQUATIONS 187(2): 429-455.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Liskevich, Vitali; Sobol, Zeev
Abstract / Bemerkung
We study the problem of existence and nonexistence of positive solutions of the semilinear elliptic inequalities in divergence form with measurable coefficients -del . a . delu + Vu - Wu(p)greater than or equal to0 in exterior domains in R-N, Ngreater than or equal to3. For W(x)asymptotic to\x\(-sigma) (sigmais an element ofR) at infinity we compute the critical line on the plane (p, a), which separates the domains of existence and nonexistence, and reveal the class of potentials V that preserves the critical line. Example are provided showing that the class of potentials is maximal possible, in certain sense. The case of (p, sigma) on the critical line has also been studied. (C) 2002 Elsevier Science (USA). All rights reserved.
Stichworte
positive solutions; semilinear elliptic equations and inequalities; critical exponent
Erscheinungsjahr
2003
Zeitschriftentitel
JOURNAL OF DIFFERENTIAL EQUATIONS
Band
187
Ausgabe
2
Seite(n)
429-455
ISSN
0022-0396
Page URI
https://pub.uni-bielefeld.de/record/1612637

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Kondratiev Y, Liskevich V, Sobol Z. Second-order semilinear elliptic inequalities in exterior domains. JOURNAL OF DIFFERENTIAL EQUATIONS. 2003;187(2):429-455.
Kondratiev, Y., Liskevich, V., & Sobol, Z. (2003). Second-order semilinear elliptic inequalities in exterior domains. JOURNAL OF DIFFERENTIAL EQUATIONS, 187(2), 429-455. https://doi.org/10.1016/S0022-0396(02)00036-0
Kondratiev, Y., Liskevich, V., and Sobol, Z. (2003). Second-order semilinear elliptic inequalities in exterior domains. JOURNAL OF DIFFERENTIAL EQUATIONS 187, 429-455.
Kondratiev, Y., Liskevich, V., & Sobol, Z., 2003. Second-order semilinear elliptic inequalities in exterior domains. JOURNAL OF DIFFERENTIAL EQUATIONS, 187(2), p 429-455.
Y. Kondratiev, V. Liskevich, and Z. Sobol, “Second-order semilinear elliptic inequalities in exterior domains”, JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 187, 2003, pp. 429-455.
Kondratiev, Y., Liskevich, V., Sobol, Z.: Second-order semilinear elliptic inequalities in exterior domains. JOURNAL OF DIFFERENTIAL EQUATIONS. 187, 429-455 (2003).
Kondratiev, Yuri, Liskevich, Vitali, and Sobol, Zeev. “Second-order semilinear elliptic inequalities in exterior domains”. JOURNAL OF DIFFERENTIAL EQUATIONS 187.2 (2003): 429-455.

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