{"title":"具有混合型参数的半线性微分方程的振动","authors":"J. Džurina, B. Baculíková","doi":"10.14232/ejqtde.2022.1.10","DOIUrl":null,"url":null,"abstract":"<jats:p>This paper is devoted to the study of the oscillatory behavior of half-linear functional differential equations with deviating argument of the form <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <mml:mtable displaystyle=\"true\"> <mml:mlabeledtr> <mml:mtd id=\"mjx-eqn-Eabs\"> <mml:mrow> <mml:mtext>(</mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>E</mml:mi> </mml:mrow> <mml:mtext>)</mml:mtext> </mml:mrow> </mml:mtd> <mml:mtd> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mi>y</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:msup> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>α<!-- α --></mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:msup> <mml:mi>y</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>α<!-- α --></mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>τ<!-- τ --></mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>.</mml:mo> </mml:mtd> </mml:mlabeledtr> </mml:mtable> </mml:math>. We introduce new technique based on monotonic properties of nonoscillatory solutions to offer new oscillatory criteria for <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow class=\"MathJax_ref\" href=\"#mjx-eqn-Eabs\"> <mml:mrow> <mml:mtext>(</mml:mtext> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>E</mml:mi> </mml:mrow> <mml:mtext>)</mml:mtext> </mml:mrow> </mml:mrow> </mml:math>. We will show that presented results essentially improve existing ones even for linear differential equations.</jats:p>","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Oscillation of half-linear differential equations with mixed type of argument\",\"authors\":\"J. 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We introduce new technique based on monotonic properties of nonoscillatory solutions to offer new oscillatory criteria for <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mrow class=\\\"MathJax_ref\\\" href=\\\"#mjx-eqn-Eabs\\\"> <mml:mrow> <mml:mtext>(</mml:mtext> <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\"> <mml:mi>E</mml:mi> </mml:mrow> <mml:mtext>)</mml:mtext> </mml:mrow> </mml:mrow> </mml:math>. 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引用次数: 2
摘要
本文研究了具有(E) (r (t) (y ' (t))形式的半线性泛函微分方程的振荡行为。α) ' = p (t) y α (τ (t))。我们引入了基于非振荡解单调性的新技术，给出了(E)的新的振荡判据。我们将证明，即使对于线性微分方程，所提出的结果本质上也改进了现有的结果。
Oscillation of half-linear differential equations with mixed type of argument
This paper is devoted to the study of the oscillatory behavior of half-linear functional differential equations with deviating argument of the form (E)(r(t)(y′(t))α)′=p(t)yα(τ(t)).. We introduce new technique based on monotonic properties of nonoscillatory solutions to offer new oscillatory criteria for (E). We will show that presented results essentially improve existing ones even for linear differential equations.
期刊介绍：
The Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE) is a completely open access journal dedicated to bringing you high quality papers on the qualitative theory of differential equations. Papers appearing in EJQTDE are available in PDF format that can be previewed, or downloaded to your computer. The EJQTDE is covered by the Mathematical Reviews, Zentralblatt and Scopus. It is also selected for coverage in Thomson Reuters products and custom information services, which means that its content is indexed in Science Citation Index, Current Contents and Journal Citation Reports. Our journal has an impact factor of 1.827, and the International Standard Serial Number HU ISSN 1417-3875.
All topics related to the qualitative theory (stability, periodicity, boundedness, etc.) of differential equations (ODE''s, PDE''s, integral equations, functional differential equations, etc.) and their applications will be considered for publication. Research articles are refereed under the same standards as those used by any journal covered by the Mathematical Reviews or the Zentralblatt (blind peer review). Long papers and proceedings of conferences are accepted as monographs at the discretion of the editors.
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