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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 2, Pages 41–126 (Mi izv235)  

This article is cited in 13 scientific papers (total in 13 papers)

On non-negative solutions of quasilinear elliptic inequalities

A. A. Kon'kov

N. E. Bauman Moscow State Technical University

Abstract: We study the solutions of the inequalities
$$ Lu\geqslant F(x,u), \qquad \mathcal Lu\geqslant F(x,u), $$
where
$$ L=\sum_{i,j=1}^n\frac\partial{\partial x_i}(a_{ij}(x)\frac\partial{\partial x_j}), \qquad \mathcal L=\sum_{i,j=1}^n a_{ij}(x)\frac{\partial^2}{\partial x_i \partial x_j} , $$
are differential operators of elliptic type and $F$ is some function.

DOI: https://doi.org/10.4213/im235

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English version:
Izvestiya: Mathematics, 1999, 63:2, 255–329

Bibliographic databases:

MSC: 35J15, 35J25, 34A34, 34C10
Received: 17.07.1997

Citation: A. A. Kon'kov, “On non-negative solutions of quasilinear elliptic inequalities”, Izv. RAN. Ser. Mat., 63:2 (1999), 41–126; Izv. Math., 63:2 (1999), 255–329

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. Mitidieri, S. I. Pokhozhaev, “Nonexistence of Positive Solutions for Quasilinear Elliptic Problems on $\mathbb R^N$”, Proc. Steklov Inst. Math., 227 (1999), 186–216  mathnet  mathscinet  zmath
    2. G. G. Laptev, “Non-existence of solutions of semilinear parabolic differential inequalities in cones”, Sb. Math., 192:10 (2001), 1471–1490  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. G. G. Laptev, “On the Absence of Solutions for a Class of Singular Semilinear Differential Inequalities”, Proc. Steklov Inst. Math., 232 (2001), 216–228  mathnet  mathscinet  zmath
    4. E. Mitidieri, S. I. Pokhozhaev, “A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities”, Proc. Steklov Inst. Math., 234 (2001), 1–362  mathnet  mathscinet  zmath
    5. Zatevakhin M.A., “Turbulent thermal in a humid atmosphere”, High Temperature, 39:4 (2001), 532–539  mathnet  crossref  isi  elib  scopus
    6. G. G. Laptev, “Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains”, Izv. Math., 66:6 (2002), 1147–1170  mathnet  crossref  crossref  mathscinet  zmath
    7. G. G. Laptev, “Nonexistence of Solutions of Elliptic Differential Inequalities in Conic Domains”, Math. Notes, 71:6 (2002), 782–793  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. A. A. Kon'kov, “Comparison theorems for elliptic inequalities with a non-linearity in the principal part”, Russian Math. Surveys, 57:3 (2002), 599–600  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. G. G. Laptev, “On the nonexistence of solutions of elliptic differential inequalities in a neighborhood of a conic point of the boundary”, Russian Math. (Iz. VUZ), 46:9 (2002), 48–57  mathnet  mathscinet  zmath  elib
    10. G. G. Laptev, “Absence of solutions to higher-order evolution differential inequalities”, Siberian Math. J., 44:1 (2003), 117–131  mathnet  crossref  mathscinet  zmath  isi
    11. A. A. Kon'kov, “Behavior of Solutions of Quasilinear Elliptic Inequalities”, Journal of Mathematical Sciences, 134:3 (2006), 2073–2237  mathnet  crossref  mathscinet  zmath  elib
    12. A. A. Kon'kov, “The behaviour of solutions of elliptic inequalities that are non-linear with respect to the highest derivatives”, Izv. Math., 71:1 (2007), 15–51  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. Mamedov F.I., Amanov R.A., “On local and global properties of solutions of semilinear equations with principal part of the type of a degenerating p-Laplacian”, Differential Equations, 43:12 (2007), 1724–1732  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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