An oscillation theorem for differential equations with deviating argument

Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument

and Applied Analysis 3 If any solution x of 1.1 is either oscillatory, or satisfies the condition 1.7 , or admits the asymptotic representation x i c 1 sin t − α i εi t , i 0, 1, 2, 3 , 1.8 where c / 0 and α are constants, the continuous functions εi i 0, 1, 2, 3 vanish at infinity and ε0 satisfies the inequality cε0 t > 0 for large t, then we say that 1.1 has weak property A. For n 3, the resu...

Oscillation of second order neutral equations with distributed deviating argument

Oscillation criteria are established for the second order neutral delay differential equation with distributed deviating argument (r(t) (x(t))Z′(t))′ + ∫ b a q(t, )f [x(g(t, ))] d ( )= 0, t t0, where Z(t)= x(t)+p(t)x(t − ). These results are extensions of the integral averaging techniques due to Coles and Kamenev, and improve some known oscillation criteria in the existing literature. © 2006 El...

Fourth-Order Differential Equation with Deviating Argument

and Applied Analysis 3 Motivated by 14, 15 , here we study the existence of AL-solutions for 1.1 . The approach is completely different from the one used in 15 , in which an iteration process, jointly with a comparison with the linear equation y 4 q t y 2 0, is employed. Our tools are based on a topological method, certain integral inequalities, and some auxiliary functions. In particular, for ...

Oscillation criteria for second-order neutral equations with distributed deviating argument

Anti-Periodic Solutions for a Class of Third-Order Nonlinear Differential Equations with a Deviating Argument

In this paper, we study a class of third-order nonlinear differential equations with a deviating argument and establish some sufficient conditions for the existence and exponential stability of anti-periodic solutions of the equation. These conditions are new and complement to previously known results.