New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations

New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations

The objective of this study is to establish new sufficient criteria for oscillation of solutions of even-order delay Emden-Fowler differential equations with neutral term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics&g...

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Autores principales: Saeed Althubiti, Ibtisam Aldawish, Jan Awrejcewicz, Omar Bazighifan
Formato: article
Lenguaje:EN
Publicado: MDPI AG 2021
Materias:
even-order differential equations
neutral delay
oscillation
Mathematics
QA1-939
Acceso en línea:https://doaj.org/article/0d4a5c5e31144acdb1641d1488e92caa
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spelling oai:doaj.org-article:0d4a5c5e31144acdb1641d1488e92caa2021-11-25T19:07:22ZNew Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations10.3390/sym131121772073-8994https://doaj.org/article/0d4a5c5e31144acdb1641d1488e92caa2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2177https://doaj.org/toc/2073-8994The objective of this study is to establish new sufficient criteria for oscillation of solutions of even-order delay Emden-Fowler differential equations with neutral term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mfenced separators="" open="(" close=")"><mi>r</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced><msup><mfenced separators="" open="(" close=")"><msup><mfenced separators="" open="(" close=")"><mi>y</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced><mo>+</mo><mi>m</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced><mi>y</mi><mfenced separators="" open="(" close=")"><mi>g</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced></mfenced></mfenced><mfenced separators="" open="(" close=")"><mi>n</mi><mo>−</mo><mn>1</mn></mfenced></msup></mfenced><mi>γ</mi></msup></mfenced><mo>′</mo></msup><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>j</mi></msubsup><msub><mi>q</mi><mi>i</mi></msub><mfenced open="(" close=")"><mi>ı</mi></mfenced><msup><mi>y</mi><mi>γ</mi></msup><mfenced separators="" open="(" close=")"><msub><mi>μ</mi><mi>i</mi></msub><mfenced open="(" close=")"><mi>ı</mi></mfenced></mfenced><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>. We use Riccati transformation and the comparison with first-order differential inequalities to obtain theses criteria. Moreover, the presented oscillation conditions essentially simplify and extend known criteria in the literature. To show the importance of our results, we provide some examples. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.Saeed AlthubitiIbtisam AldawishJan AwrejcewiczOmar BazighifanMDPI AGarticleeven-order differential equationsneutral delayoscillationMathematicsQA1-939ENSymmetry, Vol 13, Iss 2177, p 2177 (2021)
institution DOAJ
collection DOAJ
language EN
topic even-order differential equations
neutral delay
oscillation
Mathematics
QA1-939
spellingShingle even-order differential equations
neutral delay
oscillation
Mathematics
QA1-939
Saeed Althubiti
Ibtisam Aldawish
Jan Awrejcewicz
Omar Bazighifan
New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations
description The objective of this study is to establish new sufficient criteria for oscillation of solutions of even-order delay Emden-Fowler differential equations with neutral term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mfenced separators="" open="(" close=")"><mi>r</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced><msup><mfenced separators="" open="(" close=")"><msup><mfenced separators="" open="(" close=")"><mi>y</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced><mo>+</mo><mi>m</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced><mi>y</mi><mfenced separators="" open="(" close=")"><mi>g</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced></mfenced></mfenced><mfenced separators="" open="(" close=")"><mi>n</mi><mo>−</mo><mn>1</mn></mfenced></msup></mfenced><mi>γ</mi></msup></mfenced><mo>′</mo></msup><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>j</mi></msubsup><msub><mi>q</mi><mi>i</mi></msub><mfenced open="(" close=")"><mi>ı</mi></mfenced><msup><mi>y</mi><mi>γ</mi></msup><mfenced separators="" open="(" close=")"><msub><mi>μ</mi><mi>i</mi></msub><mfenced open="(" close=")"><mi>ı</mi></mfenced></mfenced><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>. We use Riccati transformation and the comparison with first-order differential inequalities to obtain theses criteria. Moreover, the presented oscillation conditions essentially simplify and extend known criteria in the literature. To show the importance of our results, we provide some examples. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.
format article
author Saeed Althubiti
Ibtisam Aldawish
Jan Awrejcewicz
Omar Bazighifan
author_facet Saeed Althubiti
Ibtisam Aldawish
Jan Awrejcewicz
Omar Bazighifan
author_sort Saeed Althubiti
title New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations
title_short New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations
title_full New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations
title_fullStr New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations
title_full_unstemmed New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations
title_sort new oscillation results of even-order emden–fowler neutral differential equations
publisher MDPI AG
publishDate 2021
url https://doaj.org/article/0d4a5c5e31144acdb1641d1488e92caa
work_keys_str_mv AT saeedalthubiti newoscillationresultsofevenorderemdenfowlerneutraldifferentialequations
AT ibtisamaldawish newoscillationresultsofevenorderemdenfowlerneutraldifferentialequations
AT janawrejcewicz newoscillationresultsofevenorderemdenfowlerneutraldifferentialequations
AT omarbazighifan newoscillationresultsofevenorderemdenfowlerneutraldifferentialequations
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