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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2005, Volume 248, Pages 164–184 (Mi tm129)  

This article is cited in 15 scientific papers (total in 16 papers)

Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems

E. Mitidieria, S. I. Pokhozhaevb

a University of Trieste
b Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: This paper is devoted to the further development of the method of nonlinear capacity in the blow-up theory for nonlinear problems. In the framework of this approach, a new class of nonlinear problems with nonlocal nonlinearities is considered, including both stationary and evolution problems. Blow-up criteria depending on the structure of the nonlinear operator and the data of the problem under study are obtained.
Received in October 2004
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: E. Mitidieri, S. I. Pokhozhaev, “Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems”, Studies on function theory and differential equations, Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 248, Nauka, MAIK «Nauka/Inteperiodika», M., 2005, 164–184; Proc. Steklov Inst. Math., 248 (2005), 158–178
Citation in format AMSBIB
\Bibitem{MitPok05}
\by E.~Mitidieri, S.~I.~Pokhozhaev
\paper Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems
\inbook Studies on function theory and differential equations
\bookinfo Collected papers. Dedicated to the 100th birthday of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2005
\vol 248
\pages 164--184
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm129}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2165926}
\zmath{https://zbmath.org/?q=an:1123.35087}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 248
\pages 158--178
Linking options:
  • https://www.mathnet.ru/eng/tm129
  • https://www.mathnet.ru/eng/tm/v248/p164
  • This publication is cited in the following 16 articles:
    1. V. I. Bogachev, S. V. Shaposhnikov, “Nonlinear Fokker–Planck–Kolmogorov equations”, Russian Math. Surveys, 79:5 (2024), 751–805  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. Yuepeng Li, Zhong Bo Fang, “Fujita type results for a parabolic differential inequality with weighted nonlocal source”, Mosc. Math. J., 23:2 (2023), 243–270  mathnet
    3. Muravnik A.B., “On Absence of Global Solutions of Quasilinear Differential-Convolutional Inequalities”, Complex Var. Elliptic Equ., 65:6 (2020), 977–985  crossref  mathscinet  isi
    4. E. I. Galakhov, O. A. Salieva, “Nonexistence of sign-changing solutions for some elliptic inequalities in bounded domains”, Comput. Math. Math. Phys., 60:8 (2020), 1331–1336  mathnet  crossref  crossref  isi  elib
    5. E. I. Galakhov, O. A. Salieva, “Otsutstvie reshenii dlya nekotorykh neodnorodnykh ellipticheskikh neravenstv”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 605–612  mathnet  crossref
    6. Lei Yu., “Qualitative Properties of Positive Solutions of Quasilinear Equations With Hardy Terms”, Forum Math., 29:5 (2017), 1177–1198  crossref  mathscinet  zmath  isi  scopus
    7. Abdelmalek S., Bajneed M., Sioud Kh., “Nonexistence of Solutions To Cauchy Problems For Fractional Time Semi-Linear Pseudo-Hyperbolic Systems”, Electron. J. Differ. Equ., 2016, 20  mathscinet  zmath  isi
    8. Sun Yu., “Uniqueness Result for Non-Negative Solutions of Semi-Linear Inequalities on Riemannian Manifolds”, J. Math. Anal. Appl., 419:1 (2014), 643–661  crossref  mathscinet  zmath  isi  elib  scopus
    9. Moroz V. Van Schaftingen J., “Nonexistence and Optimal Decay of Supersolutions to Choquard Equations in Exterior Domains”, J. Differ. Equ., 254:8 (2013), 3089–3145  crossref  mathscinet  zmath  isi  elib  scopus
    10. O. A. Manita, S. V. Shaposhnikov, “Nonlinear parabolic equations for measures”, St. Petersburg Math. J., 25:1 (2014), 43–62  mathnet  crossref  mathscinet  zmath  isi  elib
    11. Mitidieri E., Pokhozhaev S.I., “Lifespan estimates for solutions of some evolution inequalities”, Differential Equations, 45:10 (2009), 1473–1484  crossref  mathscinet  zmath  isi  elib  scopus
    12. Pohozaev S.I., “Critical Nonlinearities in Partial Differential Equations”, Milan Journal of Mathematics, 77:1 (2009), 127–150  crossref  mathscinet  zmath  isi  scopus
    13. Proc. Steklov Inst. Math., 260 (2008), 90–111  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    14. Galaktionov, VA, “CAPACITY INDUCED BY A NONLINEAR OPERATOR AND APPLICATIONS”, Georgian Mathematical Journal, 15:3 (2008), 501  crossref  mathscinet  zmath  isi
    15. Caristi, G, “Local estimates and Liouville theorems for a class of quasilinear inequalities”, Doklady Mathematics, 77:1 (2008), 85  crossref  mathscinet  zmath  isi  elib
    16. O. V. Besov, A. M. Il'in, V. A. Il'in, L. D. Kudryavtsev, S. M. Nikol'skii, L. V. Ovsyannikov, E. Mitidieri, A. Tesei, L. Véron, “Stanislav Ivanovich Pokhozhaev (on his 70th birthday)”, Russian Math. Surveys, 61:2 (2006), 373–378  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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