Ganesh Purushothaman, Kannan Suresh, Ethiraju Thandapani, Ercan Tunc
Abstract:
This article focuses on the existence and asymptotic behavior of
Kneser-type solutions to third-order noncanonical differential
equations with a delay or advanced argument in the neutral term
$$
\Big(r_2(t)\big(r_1(t)z'(t)\big)'\Big)'+g(t)x(t)=0,
$$
where \(z(t)=x(t)+p(t)x(\tau(t))\). This equation is transformed
into a canonical equation, which reduces the number of classes of
positive solutions from 4 to 2. This is done without assuming
extra conditions, and greatly simplifies the process of
obtaining conditions for the existence of Kneser-type solutions.
Also we obtain lower and upper bounds for these solutions,
and obtain their rate of convergence to zero.
Two examples are provided to illustrate our main results,
one with a delay neutral term, and one with an advanced neutral term.
Submitted July 25, 2024. Published September 19, 2024.
Math Subject Classifications: 34C10, 34K11, 34K40.
Key Words: Kneser solution; neutral differential equation; noncanonical equation.
DOI: 10.58997/ejde.2024.55
Show me the PDF file (356 KB), TEX file for this article.
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Ganesh Purushothaman Department of Mathematics St. Joseph's College of Engineering Chennai - 600119, India email: gpmanphd@gmail.com |
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Kannan Suresh Department of Mathematics St. Joseph's College of Engineering Chennai - 600119, India email: dhivasuresh@gmail.com |
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Ethiraju Thandapani Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chennai - 600005, India email: ethandapani@yahoo.co.in |
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Ercan Tunç Department of Mathematics, Faculty of Arts and Sciences Tokat Gaziosmanpasa University, 60240, Tokat, Turkiye email: ercantunc72@yahoo.com |
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