Qualitative Properties to Type of Second Order Emden-Fowler Dynamic Equation

Hadeel Saeed   Mahmoud; Aqeel Falih   Jaddoa

doi:10.30526/39.3.4436

Authors

Hadeel Saeed Mahmoud Mathematics, College of Education for Pure Sciences/ Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq. https://orcid.org/0009-0008-6179-1332
Aqeel Falih Jaddoa Mathematics, College of Education for Pure Sciences/ Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq. https://orcid.org/0000-0002-5590-7991

DOI:

https://doi.org/10.30526/39.3.4436

Keywords:

Emden-Fowler dynamic equation, Neutral type Second Order, Asymptotic Behavior, Oscillation Property, Difference Equation

Abstract

This study aimed to secure oscillation properties with asymptotic natures to solutions of Emden-Fowler dynamic equations on a time scale. The primary objectives were to establish new sufficient criteria that guarantee either the oscillatory of solutions or properties of non-oscillatory solutions in mean of asymptotic behavior, such as convergence to zero or to infinity. The research was conducted within the unified framework of difference equations. The classification principle for non-oscillatory solutions, along with the use of generalized and fundamental lemmas, was employed to derive the desired properties, including oscillation criteria and the analysis of asymptotic behavior. The analysis yielded new oscillation criteria with sufficient conditions. For the non-oscillatory case, the study provided explicit conditions under which every solution must eventually satisfy a specific asymptotic property, an illustrative example for application of new results with an effective condition.

It was concluded that the newly established criteria are both effective and widely applicable, as they extend and generalize many known results for differential and difference equations. This work provides a comprehensive theoretical framework for understanding the qualitative phenomena of this significant class of dynamic equations

Author Biographies

Hadeel Saeed Mahmoud , Mathematics, College of Education for Pure Sciences/ Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq.

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Aqeel Falih Jaddoa, Mathematics, College of Education for Pure Sciences/ Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq.

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