Sup erlinear elliptic inequalities on manifolds

Grigoryan A, Sun Y, Verbitsky I (2020)
JOURNAL OF FUNCTIONAL ANALYSIS 278(9): UNSP 108444.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Grigoryan, AlexanderUniBi; Sun, Yuhua; Verbitsky, Igor
Abstract / Bemerkung
Let M be a complete non-compact Riemannian manifold and let alpha be a Radon measure on M. We study the problem of existence or non-existence of positive solutions to a semilinear elliptic inequality Delta u >= sigma u(q) in M, where q > 1. We obtain necessary and sufficient criteria for existence of positive solutions in terms of Green function of A. In particular, explicit necessary and sufficient conditions are given when M has nonnegative Ricci curvature everywhere in M, or more generally when Green's function satisfies the 3G-inequality. (C) 2019 Elsevier Inc. All rights reserved.
Stichworte
Semilinear elliptic equations; Green's function; Complete Riemannian; manifold
Erscheinungsjahr
2020
Zeitschriftentitel
JOURNAL OF FUNCTIONAL ANALYSIS
Band
278
Ausgabe
9
Art.-Nr.
UNSP 108444
ISSN
0022-1236
eISSN
1096-0783
Page URI
https://pub.uni-bielefeld.de/record/2941868

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Grigoryan A, Sun Y, Verbitsky I. Sup erlinear elliptic inequalities on manifolds. JOURNAL OF FUNCTIONAL ANALYSIS. 2020;278(9): UNSP 108444.
Grigoryan, A., Sun, Y., & Verbitsky, I. (2020). Sup erlinear elliptic inequalities on manifolds. JOURNAL OF FUNCTIONAL ANALYSIS, 278(9), UNSP 108444. doi:10.1016/j.jfa.2019.108444
Grigoryan, A., Sun, Y., and Verbitsky, I. (2020). Sup erlinear elliptic inequalities on manifolds. JOURNAL OF FUNCTIONAL ANALYSIS 278:UNSP 108444.
Grigoryan, A., Sun, Y., & Verbitsky, I., 2020. Sup erlinear elliptic inequalities on manifolds. JOURNAL OF FUNCTIONAL ANALYSIS, 278(9): UNSP 108444.
A. Grigoryan, Y. Sun, and I. Verbitsky, “Sup erlinear elliptic inequalities on manifolds”, JOURNAL OF FUNCTIONAL ANALYSIS, vol. 278, 2020, : UNSP 108444.
Grigoryan, A., Sun, Y., Verbitsky, I.: Sup erlinear elliptic inequalities on manifolds. JOURNAL OF FUNCTIONAL ANALYSIS. 278, : UNSP 108444 (2020).
Grigoryan, Alexander, Sun, Yuhua, and Verbitsky, Igor. “Sup erlinear elliptic inequalities on manifolds”. JOURNAL OF FUNCTIONAL ANALYSIS 278.9 (2020): UNSP 108444.