الفهرس | Only 14 pages are availabe for public view |
Abstract the oscillatory behavior of solutions of different classes of differential and dynamic equations is discussed. We first start with the second order nonlinear differential equations ( ( ) ( ( ) ( ))) ′ ( ) ( ( ) ( )) ( ) ( ) ( ( )) , Secondly, we consider the third order nonlinear differential equations of the type ( ( ) ′′( )) ′ ( ( ) ( )) and establish new sufficient conditions for oscillation of solutions. Then we consider the more general third order nonlinear differential equation ( ( ) ( ( )) ( )) ( ( ) ( )) Further, we consider the new trend recently appeared, namely the so called dynamic equations on time scales which unify both differential equations and difference equations We are mainly concerned with the oscillatory behavior of solutions of the class of nonlinear second-order damped dynamic equations ( ( ) ( ( )) ( )) ( ) ( ) ( ) ( ( )) Then we discuss interval oscillation criteria of nonlinear damped second-order dynamic equations on time scales of the type ( ( ) ( )) ( ) ( ) ( ( ) ( )) ) and the more general damped dynamic equation ( ( ) ( ( )) ( )) ( ) ( ) ( ( ) ( )) The obtained results improve and extend some known results in the literature. Sufficient conditions are given for the oscillatory behavior of solutions of nonlinear dynamic and differential equations. Finally we give some examples that justify our results. |