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Mat. Sb., 2010, Volume 201, Number 6, Pages 75–92 (Mi msb7585)  

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

Nonnegative solutions of some quasilinear elliptic inequalities and applications

L. D'Ambrosioa, E. Mitidierib

a Department of Mathematics, University of Bari, Italy
b Department of Mathematics and Informatics, University of Trieste, Italy

Abstract: Let $f\colon \mathbb R\to\mathbb R$ be a continuous function. It is shown that under certain assumptions on $f$ and $A\colon \mathbb R\to\mathbb R_+$ weak $\mathscr C^1$ solutions of the differential inequality $-\operatorname{div}(A(|\nabla u|)\nabla u)\ge f(u)$ on $\mathbb R^N$ are nonnegative. Some extensions of the result in the framework of subelliptic operators on Carnot groups are considered.
Bibliography: 19 titles.

Keywords: differential inequalities, $p$-Laplacian, nonnegative solutions, subelliptic operators, Carnot groups.


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English version:
Sbornik: Mathematics, 2010, 201:6, 855–871

Bibliographic databases:

UDC: 517.956.25
MSC: 35R45, 35J60
Received: 07.05.2009

Citation: L. D'Ambrosio, E. Mitidieri, “Nonnegative solutions of some quasilinear elliptic inequalities and applications”, Mat. Sb., 201:6 (2010), 75–92; Sb. Math., 201:6 (2010), 855–871

Citation in format AMSBIB
\by L.~D'Ambrosio, E.~Mitidieri
\paper Nonnegative solutions of some quasilinear elliptic inequalities and applications
\jour Mat. Sb.
\yr 2010
\vol 201
\issue 6
\pages 75--92
\jour Sb. Math.
\yr 2010
\vol 201
\issue 6
\pages 855--871

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    This publication is cited in the following articles:
    1. D'Ambrosio L., Mitidieri E., “A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities”, Adv. Math., 224:3 (2010), 967–1020  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. Filippucci R., “Nonexistence of nonnegative solutions of elliptic systems of divergence type”, J. Differ. Equations, 250:1 (2011), 572–595  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. Li X., Li F., “Nonexistence of solutions for singular quasilinear differential inequalities with a gradient nonlinearity”, Nonlinear Anal., 75:5 (2012), 2812–2822  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Brandolini L., Magliaro M., “A note on Keller-Osserman conditions on Carnot groups”, Nonlinear Anal., 75:4 (2012), 2326–2337  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Li X., Li F., “Nonexistence of solutions for nonlinear differential inequalities with gradient nonlinearities”, Commun. Pure Appl. Anal., 11:3 (2012), 935–943  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. D'Ambrosio L., Mitidieri E., “A Priori Estimates and Reduction Principles for Quasilinear Elliptic Problems and Applications”, Adv. Differ. Equat., 17:9–10 (2012), 935–1000  mathscinet  zmath  isi
    7. Proc. Steklov Inst. Math., 283 (2013), 3–19  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. D'Ambrosio L., Farina A., Mitidieri E., Serrin J., “Comparison Principles, Uniqueness and Symmetry Results of Solutions of Quasilinear Elliptic Equations and Inequalities”, Nonlinear Anal.-Theory Methods Appl., 90 (2013), 135–158  crossref  mathscinet  zmath  isi  scopus  scopus
    9. D'Ambrosio L., Mitidieri E., “An Application of Kato's Inequality to Quasilinear Elliptic Problems”, Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems, Contemporary Mathematics, 595, eds. Serrin J., Mitidieri E., Radulescu V., Amer Mathematical Soc, 2013, 205–218  crossref  mathscinet  zmath  isi
    10. Li X., “Positivity and Nonexistence of Solutions For Quasilinear Inequalities”, Electron. J. Differ. Equ., 2016, 175  mathscinet  isi
    11. Li X., “Non-existence of solutions for nonlinear differential inequalities with singularities on the boundary”, Complex Var. Elliptic Equ., 62:6 (2017), 748–759  crossref  mathscinet  zmath  isi  scopus
    12. D'Ambrosio L., Mitidieri E., “Quasilinear Elliptic Equations With Critical Potentials”, Adv. Nonlinear Anal., 6:2 (2017), 147–164  crossref  mathscinet  zmath  isi  scopus
    13. D'Ambrosio L., Mitidieri E., “Uniqueness and Comparison Principles For Semilinear Equations and Inequalities in Carnot Groups”, Adv. Nonlinear Anal., 7:3 (2018), 313–325  crossref  mathscinet  zmath  isi  scopus
    14. Georgiev V., Tarulli M., Venkov G., “Existence and Uniqueness of Ground States For P-Choquard Model”, Nonlinear Anal.-Theory Methods Appl., 179 (2019), 131–145  crossref  mathscinet  zmath  isi  scopus
    15. D'Ambrosio L., Mitidieri E., “Representation Formulae of Solutions of Second Order Elliptic Inequalities”, Nonlinear Anal.-Theory Methods Appl., 178 (2019), 310–336  crossref  mathscinet  zmath  isi  scopus
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