Abstract
AbstractThis paper deals with oscillation of a second order delay differential equations with a nonlinear nonpositive neutral term. Some new oscillation criteria and three examples are presented which improve and generalize the results reported in the literature.
Highlights
We study the oscillatory behavior of a second order nonlinear neutral delay differential equations of the form (a(t)(x(t) − p(t)xα(τ (t))) ) + q(t)xβ(σ(t)) = 0, t ≥ t0 > 0 (1.1)
We choose to investigate the oscillatory behavior of solutions of equation (1.1) since similar properties for delay differential equations with linear neutral term are studied in many papers, see [1, 3,4,5,6, 10,11,12,13, 16, 17] and the references cited therein
Further note that the results reported in [7, 11, 13, 17] cannot be applied to equations (3.1), (3.2) and (3.3) since the neutral term is not linear
Summary
We study the oscillatory behavior of a second order nonlinear neutral delay differential equations of the form (a(t)(x(t) − p(t)xα(τ (t))) ) + q(t)xβ(σ(t)) = 0, t ≥ t0 > 0. We choose to investigate the oscillatory behavior of solutions of equation (1.1) since similar properties for delay differential equations with linear neutral term are studied in many papers, see [1, 3,4,5,6, 10,11,12,13, 16, 17] and the references cited therein. In [2, 14], the authors considered equation (1.1) with p(t) < 0 for all t ≥ t0, and established criteria for the oscillation of all solutions under the following condition. Motivated by the above observation, in this paper we derive some new oscillation results for the equation (1.1), which improve and complement those reported in [2, 11, 13,14,15]
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