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: | , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/0d4a5c5e31144acdb1641d1488e92caa |
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| Sumario: | 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. |
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