<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Some new oscillation criteria are obtained for a class of thirdorder quasi-linear Emden-Fowler differential equations with unbounded neutral coefficients of the form
<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/tmmp-2021-0028_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msup><mrow><mo stretchy="false">(</mo><mi>z</mi><mo>″</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><mi>α</mi></msup><mo stretchy="false">)</mo><mo>′</mo><mo>+</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><msup><mi>y</mi><mi>λ</mi></msup><mo stretchy="false">(</mo><mi>g</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math><tex-math>\[(a(t){(z(t))^\alpha })' + f(t){y^\lambda }(g(t)) = 0,\]</tex-math></alternatives></inline-formula> where <italic>z</italic>(<italic>t</italic>) = <italic>y</italic>(<italic>t</italic>) + <italic>p</italic>(<italic>t</italic>)<italic>y</italic>(<italic>σ</italic>(<italic>t</italic>)) and <italic>α, λ</italic> are ratios of odd positive integers. The established results generalize, improve and complement to known results.</p>
</abstract>

Some new oscillation criteria are obtained for a class of thirdorder quasi-linear Emden-Fowler differential equations with unbounded neutral coefficients of the form
(a(t)(z″(t))α)′+f(t)yλ(g(t))=0,\[(a(t){(z(t))^\alpha })' + f(t){y^\lambda }(g(t)) = 0,\] where z(t) = y(t) + p(t)y(σ(t)) and α, λ are ratios of odd positive integers. The established results generalize, improve and complement to known results.

Oscillation Results for Third-Order Quasi-Linear Emden-Fowler Differential Equations with Unbounded Neutral Coefficients

School of Pedagogical and Technological Education

Ramanujan Institute for Advanced Study in Mathematics, University of Madras

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Some new oscillation criteria are obtained for a class of thirdorder quasi-linear Emden-Fowler differential equations with unbounded neutral coefficients of...

Oscillation Results for Third-Order Quasi-Linear Emden-Fowler Differential Equations with Unbounded Neutral Coefficients

Published Online: Jan 01, 2022

Page range: 1 - 14

Received: Mar 17, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0028

Keywords
quasi-linear, neutral differential equation, Emden-Fowler differential equation, oscillation

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Oscillation Results for Third-Order Quasi-Linear Emden-Fowler Differential Equations with Unbounded Neutral Coefficients

Published Online: Jan 01, 2022

Page range: 1 - 14

Received: Mar 17, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0028

Keywordsquasi-linear, neutral differential equation, Emden-Fowler differential equation, oscillation

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
quasi-linear, neutral differential equation, Emden-Fowler differential equation, oscillation