J. Hay, “On Necessary Conditions for the Existence of Local Solutions to Singular Nonlinear Ordinary Differential Equations and Inequalities”, Mat. Zametki, 72:6 (2002), 924–935; Math. Notes, 72:6 (2002), 847

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Matematicheskie Zametki, 2002, Volume 72, Issue 6, Pages 924–935
DOI: https://doi.org/10.4213/mzm478 (Mi mzm478)

This article is cited in 6 scientific papers (total in 6 papers)

On Necessary Conditions for the Existence of Local Solutions to Singular Nonlinear Ordinary Differential Equations and Inequalities

J. Hay

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (197 kB) Citations (6)

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DOI: https://doi.org/10.4213/mzm478

Abstract: We obtain conditions for the nonexistence of global solutions and estimates of existence time for local solutions to the problem

$\frac {d^ky}{dt^k} \ge a_1(t)|y|^{q_1}+a_2(t)|y|^{q_2}+\dots +a_n(t)|y|^{q_n}.$
The proofs are based on the method of trial functions developed by Mitidieri and Pokhozhaev.

Received: 03.07.2002

English version:
Mathematical Notes, 2002, Volume 72, Issue 6, Pages 847–857
DOI: https://doi.org/10.1023/A:1021498114996

Bibliographic databases:

UDC: 517.9

Language: Russian

Citation: J. Hay, “On Necessary Conditions for the Existence of Local Solutions to Singular Nonlinear Ordinary Differential Equations and Inequalities”, Mat. Zametki, 72:6 (2002), 924–935; Math. Notes, 72:6 (2002), 847–857

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm478

https://doi.org/10.4213/mzm478

https://www.mathnet.ru/eng/mzm/v72/i6/p924

This publication is cited in the following 6 articles:

Xiaohong Li, Haitao Wan, Xiliang Li, “Absence of Solutions for a System of Ordinary Differential Inequalities”, Math. Notes, 109:4 (2021), 600–608
Korpusov M., Ovchinnikov A., Sveshnikov A., Yushkov E., “Blow-Up in Nonlinear Equations of Mathematical Physics: Theory and Methods”, Blow-Up in Nonlinear Equations of Mathematical Physics: Theory and Methods, de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter Gmbh, 2018, 1–326
Galakhov E.I., “On the Solvability of Nonlinear Differential Inequalities with Singular Coefficients”, Differ. Equ., 49:1 (2013), 45–58
E. I. Galakhov, “On higher order elliptic and parabolic inequalities with singularities on the boundary”, Proc. Steklov Inst. Math., 269 (2010), 76–84
E. I. Galakhov, “Elliptic and parabolic inequalities with point singularities on the boundary”, Sb. Math., 200:10 (2009), 1417–1437
E. I. Galakhov, “On Differential Inequalities with Point Singularities on the Boundary”, Proc. Steklov Inst. Math., 260 (2008), 112–122

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

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Full-text PDF :	186
References:	45
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