Oscillatory criteria 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...

On Proper Oscillatory and Vanishing at Infinity Solutions of Differential Equations with a Deviating Argument

Sufficient conditions are found for the existence of multiparametrical families of proper oscillatory and vanishing-at-infinity solutions of the differential equation u(n)(t) = g ( t, u(τ0(t)), . . . , u(τm−1(t)) ) , where n ≥ 4, m is the integer part of 2 , g : R+ × R m → R is a function satisfying the local Carathéodory conditions, and τi : R+ → R (i = 0, . . . , m− 1) are measurable function...

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

OSCILLATORY CRITERIA FOR NONLINEAR nTH-ORDER DIFFERENTIAL EQUATIONS WITH QUASIDERIVATIVES

Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivatives Lny = f(t, L0y, . . . , Ln−1y) under the validity of the sign condition f(t, x1, . . . , xn)x1 ≤ 0, f(t, 0, x2, . . . , xn) = 0 on R+ × Rn.