Extended Approach to the Asymptotic Behavior and Symmetric Solutions of Advanced Differential Equations

oleh: Omar Bazighifan, Ali Hasan Ali, Fatemah Mofarreh, Youssef N. Raffoul

Format: Article
Diterbitkan: MDPI AG 2022-03-01

Deskripsi

We studied the asymptotic behavior of fourth-order advanced differential equations of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mfenced separators="" open="(" close=")"><mi>a</mi><mfenced open="(" close=")"><mi>υ</mi></mfenced><msup><mfenced separators="" open="(" close=")"><msup><mi>w</mi><mrow><mo>′</mo><mo>′</mo><mo>′</mo></mrow></msup><mfenced open="(" close=")"><mi>υ</mi></mfenced></mfenced><mi>β</mi></msup></mfenced><mo>′</mo></msup><mo>+</mo><mi>q</mi><mfenced open="(" close=")"><mi>υ</mi></mfenced><mi>g</mi><mfenced separators="" open="(" close=")"><mi>w</mi><mfenced separators="" open="(" close=")"><mi>δ</mi><mfenced open="(" close=")"><mi>υ</mi></mfenced></mfenced></mfenced><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>. New results are presented for the oscillatory behavior of these equations in the form of Philos-type and Hille–Nehari oscillation criteria. Some illustrative examples are presented.