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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2001, Volume 232, Pages 248–267 (Mi tm217)  

This article is cited in 27 scientific papers (total in 28 papers)

Nonexistence of Weak Solutions for Some Degenerate and Singular Hyperbolic Problems on Rn+1+

E. Mitidieria, S. I. Pohozaevb

a Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Via A. Valerio 12/1, 34127, Trieste, Italia
b Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: Theorems concerning the absence of weak solutions are proved for a wide class of evolution equations and inequalities. This class includes, in particular, the inequalities with degenerate and singular operators of hyperbolic type.
Received in August 2000
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: E. Mitidieri, S. I. Pohozaev, “Nonexistence of Weak Solutions for Some Degenerate and Singular Hyperbolic Problems on Rn+1+”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 232, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 248–267; Proc. Steklov Inst. Math., 232 (2001), 240–259
Citation in format AMSBIB
\Bibitem{MitPok01}
\by E.~Mitidieri, S.~I.~Pohozaev
\paper Nonexistence of Weak Solutions for Some Degenerate and Singular Hyperbolic Problems on $\mathbb R_+^{n+1}$
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 248--267
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm217}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1851453}
\zmath{https://zbmath.org/?q=an:1032.35138}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 240--259
Linking options:
  • https://www.mathnet.ru/eng/tm217
  • https://www.mathnet.ru/eng/tm/v232/p248
  • This publication is cited in the following 28 articles:
    1. Alazman I., Jleli M., Samet B., “On the Absence of Global Solutions to Two-Times-Fractional Differential Inequalities Involving Hadamard-Caputo and Caputo Fractional Derivatives”, AIMS Math., 7:4 (2022), 5830–5843  crossref  mathscinet  isi
    2. D'Abbicco M., Fujiwara K., “A Test Function Method For Evolution Equations With Fractional Powers of the Laplace Operator”, Nonlinear Anal.-Theory Methods Appl., 202 (2021), 112114  crossref  mathscinet  isi
    3. Jleli M., Samet B., “Sufficient Criteria For the Absence of Global Solutions For An Inhomogeneous System of Fractional Differential Equations”, Mathematics, 8:1 (2020), 9  crossref  isi
    4. Jleli M., Kirane M., Samet B., “Solution Blow-Up For a Fractional in Time Acoustic Wave Equation”, Math. Meth. Appl. Sci., 43:10 (2020), 6566–6575  crossref  mathscinet  isi
    5. M. O. Korpusov, “Solution blowup for nonlinear equations of the Khokhlov–Zabolotskaya type”, Theoret. and Math. Phys., 194:3 (2018), 347–359  mathnet  crossref  crossref  mathscinet  isi  elib
    6. D'Abbicco M., Ebert M.R., “A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations”, Nonlinear Anal.-Theory Methods Appl., 149 (2017), 1–40  crossref  mathscinet  zmath  isi  scopus
    7. Jleli M., Samet B., “Liouville-Type Theorems For a System Governed By Degenerate Elliptic Operators of Fractional Orders”, Arabian J. Math., 6:3 (2017), 201–211  crossref  mathscinet  zmath  isi
    8. Sun F., Shi P., “Global Existence and Non-Existence for a Higher-Order Parabolic Equation with Time-Fractional Term”, Nonlinear Anal.-Theory Methods Appl., 75:10 (2012), 4145–4155  crossref  mathscinet  zmath  isi  scopus
    9. Galaktionov V.A., Mitidieri E., Pohozaev S.I., “Capacity induced by a nonlinear operator and applications”, Georgian Math. J., 15:3 (2008), 501–516  crossref  mathscinet  zmath  isi
    10. M. Kirane, N.-e. Tatar, “Nonexistence for the Laplace equation with a dynamical boundary condition of fractional type”, Siberian Math. J., 48:5 (2007), 849–856  mathnet  crossref  mathscinet  zmath  isi
    11. 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
    12. Lupo D., Payne K.R., Popivanov N.I., “Nonexistence of nontrivial solutions for supercritical equations of mixed elliptic-hyperbolic type”, Contributions to Nonlinear Analysis - A TRIBUTE TO D. G. DE FIGUEIREDO ON THE OCCASION OF HIS 70TH BIRTHDAY, Progress in Nonlinear Differential Equations and their Applications, 66, 2006, 371–390  crossref  mathscinet  zmath  isi  scopus  scopus
    13. El Hamidi A., Laptev G.G., “Existence and nonexistence results for higher-order semilinear evolution inequalities with critical potential”, J. Math. Anal. Appl., 304:2 (2005), 451–463  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    14. Kaikina E.I., Naumkin P.I., Shishmarev I.A., “On the asymptotic behavior of solutions to the Cauchy problem for a nonlinear Sobolev-type equation”, Dokl. Math., 71:2 (2005), 269–273  mathscinet  zmath  isi  elib
    15. El Hamidi A., Laptev G.G., “Nonexistence of solutions to semilinear inequalities in conical domains”, Bull. Belg. Math. Soc. Simon Stevin, 11:3 (2004), 343–364  crossref  mathscinet  zmath  isi
    16. G. G. Laptev, “Non-existence of global solutions for higher-order evolution inequalities in unbounded cone-like domains”, Mosc. Math. J., 3:1 (2003), 63–84  mathnet  crossref  mathscinet  zmath
    17. D'Ambrosio L., Lucente S., “Nonlinear Liouville theorems for Grushin and Tricomi operators”, J. Differential Equations, 193:2 (2003), 511–541  crossref  mathscinet  zmath  isi  scopus  scopus
    18. Hay J., “Necessary conditions for the existence of local solutions to higher-order singular nonlinear ordinary differential equations and inequalities”, Dokl. Math., 67:1 (2003), 66–69  mathnet  mathscinet  zmath  isi
    19. Lupo D., Payne K.R., “Critical exponents for semilinear equations of mixed elliptic-hyperbolic and degenerate types”, Comm. Pure Appl. Math., 56:3 (2003), 403–424  crossref  mathscinet  zmath  isi  scopus  scopus
    20. Pohozaev S., “The general blow-up for nonlinear PDE's”, Function Spaces, Differential Operators and Nonlinear Analysis: the Hans Triebel Anniversary Volume, 2003, 141–159  crossref  mathscinet  zmath  isi
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