G. G. Laptev, “On the Absence of Solutions for a Class of Singular Semilinear Differential Inequalities”, 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, 223–235; Proc. Steklov Inst. Math., 232 (2001), 216

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2001, Volume 232, Pages 223–235 (Mi tm215)

This article is cited in 34 scientific papers (total in 34 papers)

On the Absence of Solutions for a Class of Singular Semilinear Differential Inequalities

G. G. Laptev

Tula State University

Full-text PDF (216 kB) Citations (34)

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Abstract: The nonexistence of solutions to certain semilinear differential inequalities in a bounded domain is established. A model problem for such inequalities is

$-\Delta u\ge |u|^q/|x|^\sigma$ (

$\sigma \ge 2$ ) in a ball

$B_R$ . Similar evolution inequalities and fourth-order problems with the operator

$\Delta ^2$ are analyzed. The proofs are based on the method of test functions.

Received in October 2000

Bibliographic databases:

UDC: 517

Language: Russian

Citation: G. G. Laptev, “On the Absence of Solutions for a Class of Singular Semilinear Differential Inequalities”, 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, 223–235; Proc. Steklov Inst. Math., 232 (2001), 216–228

Citation in format AMSBIB

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\by G.~G.~Laptev

\paper On the Absence of Solutions for a~Class of Singular Semilinear Differential Inequalities

\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 223--235

\publ Nauka, MAIK «Nauka/Inteperiodika»

\publaddr M.

\mathnet{http://mi.mathnet.ru/tm215}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1851451}

\zmath{https://zbmath.org/?q=an:1253.35227}

\transl

\jour Proc. Steklov Inst. Math.

\yr 2001

\vol 232

\pages 216--228

Linking options:

https://www.mathnet.ru/eng/tm215

https://www.mathnet.ru/eng/tm/v232/p223

This publication is cited in the following 34 articles:

Sh. G. Bagyrov, “Nonexistence of Solutions of a Semilinear Biharmonic Equation with Singular Potential”, Math. Notes, 103:1 (2018), 24–32
Bagirov Sh., “Nonexistence of Global Solutions to the System of Semilinear Parabolic Equations With Biharmonic Operator and Singular Potential”, Electron. J. Differ. Equ., 2018, 09
Li X., “Non-existence of solutions for nonlinear differential inequalities with singularities on the boundary”, Complex Var. Elliptic Equ., 62:6 (2017), 748–759
Li X., “Positivity and Nonexistence of Solutions For Quasilinear Inequalities”, Electron. J. Differ. Equ., 2016, 175
S. G. Pyatkov, S. N. Shergin, “On some mathematical models of filtration theory”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:2 (2015), 105–116
Li X., “Nonexistence of Solutions For Singular Nonlinear Ordinary Inequalities”, Electron. J. Qual. Theory Differ., 2015, no. 67
Galakhov E.I., “O razreshimosti nelineinykh differentsialnykh neravenstv s singulyarnymi koeffitsientami”, Differentsialnye uravneniya, 49:1 (2013), 46–46
Li X., Li F., “Nonexistence of solutions for singular quasilinear differential inequalities with a gradient nonlinearity”, Nonlinear Analysis-Theory Methods & Applications, 75:5 (2012), 2812–2822
Li X., Li F., “Nonexistence of Solutions for Nonlinear Differential Inequalities with Gradient Nonlinearities”, Commun. Pure Appl. Anal, 11:3 (2012), 935–943
Li X., Li F., “A priori estimates for nonlinear differential inequalities and applications”, J Math Anal Appl, 378:2 (2011), 723–733
Volodin Yu.V., “Ob otsutstvii globalnykh reshenii polulineinykh evolyutsionnykh kraevykh zadach vysokogo poryadka”, Uchenye zapiski Rossiiskogo gosudarstvennogo sotsialnogo universiteta, 2011, no. 9, 9–16
M. O. Korpusov, A. G. Sveshnikov, ““Destruction” of the solution of a strongly nonlinear equation of pseudoparabolic type with double nonlinearity”, Math. Notes, 79:6 (2006), 820–840
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
M. O. Korpusov, A. G. Sveshnikov, “On the blowup of solutions to semilinear pseudoparabolic equations with rapidly growing nonlinearities”, Comput. Math. Math. Phys., 45:1 (2005), 138–148
A. A. Kon'kov, “Behavior of Solutions of Quasilinear Elliptic Inequalities”, Journal of Mathematical Sciences, 134:3 (2006), 2073–2237
M. O. Korpusov, “Blow-up of solutions of a class of strongly non-linear equations of Sobolev type”, Izv. Math., 68:4 (2004), 783–832
Galakhov E.I., “Positive solutions of some semilinear differential inequalities and systems”, Differ. Equ., 40:5 (2004), 711–722
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
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
G. G. Laptev, “Absence of solutions to higher-order evolution differential inequalities”, Siberian Math. J., 44:1 (2003), 117–131

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

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