On the Explicit Integration of Special types of Differential Inequalities

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On the Explicit Integration of Special types of Differential Inequalities. / Ильин, Юрий Анатольевич.

In: Vestnik St. Petersburg University: Mathematics, Vol. 52, No. 2, 2019, p. 136-144.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{1abccc6b57be4f228be085f322683e53,

title = "On the Explicit Integration of Special types of Differential Inequalities",

abstract = "A general method was proposed in our previous paper for explicitly finding all solutions of the differential inequality, which is based on the general solution of the corresponding differential equation or, in other words, on the variation of arbitrary constants. Criteria of extendibility and characteristics of the maximally extended (full) solution of the inequality were proven. In this paper, we applied these results to specific types of inequalities most frequently encountered in applications and literature. We also compared them to other known methods in the literature.",

keywords = "differential inequalities, integration of special types, Differential inequality, linear differential inequality, integrable differential inequality, comparison theorems, general solution, variation method, solution continuity",

author = "Ильин, {Юрий Анатольевич}",

note = "Iljin Yu.A. On the Explicit Integration of Special types of Differential Inequalities, Vestnik St. Petersburg University, Mathemetics, 2019, Vol. 52 (2), pp. 136-144. ",

year = "2019",

language = "English",

volume = "52",

pages = "136--144",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - On the Explicit Integration of Special types of Differential Inequalities

AU - Ильин, Юрий Анатольевич

N1 - Iljin Yu.A. On the Explicit Integration of Special types of Differential Inequalities, Vestnik St. Petersburg University, Mathemetics, 2019, Vol. 52 (2), pp. 136-144.

PY - 2019

Y1 - 2019

N2 - A general method was proposed in our previous paper for explicitly finding all solutions of the differential inequality, which is based on the general solution of the corresponding differential equation or, in other words, on the variation of arbitrary constants. Criteria of extendibility and characteristics of the maximally extended (full) solution of the inequality were proven. In this paper, we applied these results to specific types of inequalities most frequently encountered in applications and literature. We also compared them to other known methods in the literature.

AB - A general method was proposed in our previous paper for explicitly finding all solutions of the differential inequality, which is based on the general solution of the corresponding differential equation or, in other words, on the variation of arbitrary constants. Criteria of extendibility and characteristics of the maximally extended (full) solution of the inequality were proven. In this paper, we applied these results to specific types of inequalities most frequently encountered in applications and literature. We also compared them to other known methods in the literature.

KW - differential inequalities

KW - integration of special types

KW - Differential inequality

KW - linear differential inequality

KW - integrable differential inequality

KW - comparison theorems

KW - general solution

KW - variation method

KW - solution continuity

UR - https://link.springer.com/article/10.1134/S1063454119020079

M3 - Article

VL - 52

SP - 136

EP - 144

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 49233761