Oscillation Behavior of Third-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

• Main Authors: Zhang Chenghui, Han Zhenlai, Li Tongxing, Sun Shurong
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Advances in Difference Equations
• Online Access: http://www.advancesindifferenceequations.com/content/2010/586312

<p/> <p>We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations <inline-formula><graphic file="1687-1847-2010-586312-i1.gif"/></inline-formula> on a time scale <inline-formula><graphic file="1687-1847-2010-586312-i2.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2010-586312-i3.gif"/></inline-formula> is a quotient of odd positive integers with <inline-formula><graphic file="1687-1847-2010-586312-i4.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-586312-i5.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2010-586312-i6.gif"/></inline-formula> real-valued positive rd-continuous functions defined on <inline-formula><graphic file="1687-1847-2010-586312-i7.gif"/></inline-formula>. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study. Some examples are considered to illustrate the main results.</p>