Oscillatory Solutions to Neutral Delay Differential Equations

• Main Authors: Fahad Alsharari, Omar Bazighifan, Taher A. Nofal, Khaled Mohamed Khedher, Youssef N. Raffoul
• Format: Article
• Language: English
• Published: MDPI AG 2021-03-01
• Series: Mathematics
• Subjects: oscillation; even-order
• Online Access: https://www.mdpi.com/2227-7390/9/7/714
• ISSN: 2227-7390

This article aims to mark out new conditions for oscillation of the even-order Emden–Fowler neutral delay 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=")"><msub><mi>β</mi><mn>1</mn></msub><mfenced open="(" close=")"><mi>ı</mi></mfenced><msub><mo>Φ</mo><mi>α</mi></msub><mrow><mo>[</mo><msup><mi>ζ</mi><mfenced separators="" open="(" close=")"><mi>r</mi><mo>−</mo><mn>1</mn></mfenced></msup><mfenced open="(" close=")"><mi>ı</mi></mfenced><mo>]</mo></mrow></mfenced><mo>′</mo></msup><mo>+</mo><msub><mi>β</mi><mn>3</mn></msub><mfenced open="(" close=")"><mi>ı</mi></mfenced><msub><mo>Φ</mo><mi>α</mi></msub><mrow><mo>[</mo><mi>ς</mi><mfenced separators="" open="(" close=")"><mi>ξ</mi><mfenced open="(" close=")"><mi>ı</mi></mfenced></mfenced><mo>]</mo></mrow><mo>=</mo><mn>0</mn><mo>.</mo></mrow></semantics></math></inline-formula> The obtained results extend, and simplify known conditions in the literature. The results are illustrated with examples.