Oscillation of third-order nonlinear functional differential equations with mixed arguments

Abstract

The objective of this paper is to offer sufficient conditions for the oscillation of all solutions and other asymptotic properties of the third-order nonlinear functional differential equationwith mixed arguments, where both cases ∞ a −1/γ (s) ds = ∞ and ∞ a −1/γ (s) ds < ∞ are dealt with. We deduce properties of the studied equations via new comparison theorems. Our results essentially improve and complement earlier ones. We also repair one interesting result of Grace et al.

Oscillation of third order differential equation with damping term

“…The aim of this paper is to investigate oscillatory and asymptotic properties of solutions to the third order nonlinear differential equation with a damping term (1) x ′′′ (t) + q(t)x ′ (t) + r(t)|x| λ (t) sgn x(t) = 0, t 0 where λ > 0, q ∈ C 2 (R + ) and r ∈ C(R + ) are positive functions on R + , R + = [0, ∞).…”

“…The asymptotic and oscillatory properties of solutions for equation (1) have been deeply investigated in literature. The pioneering work is due to M. Švec [20] and G. Villari [22] for the two-term linear differential equation…”

“…Special attention has been paid to the third order equations with quasi-derivatives, see e.g. [11], [10], with damping term [5], [9], [7] or with deviating argument [1] and the references therein.…”

Asymptotic Properties of Solutions to Third-Order Nonlinear Neutral Differential Equations

“…Recently, great attention has been devoted to the oscillation of various classes of differential equations. See, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Hartman and Wintner [1] and Erbe et al [3] studied the third-order differential equation…”

Oscillatory behavior of solutions of certain third order mixed neutral differential equations

“…(H 1 ) a(t ) is a positive nondecreasing continuous function for all t ≥ t 0 with Recently there has been a great interest in studying the oscillatory and asymptotic behavior of differential equations, see for example [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] and the references cited therein. Especially the equation 1.1with c(t ) ≡ 0 and p(t ) ≡ 0 have been the subject of intensive research.…”