Displaying similar documents to “On the oscillatory properties of the solutions of a class of integro- differential equations of neutral type.”

Existence of nonoscillatory and oscillatory solutions of neutral differential equations with positive and negative coefficients

John R. Graef, Bo Yang, Bing Gen Zhang (1999)

Mathematica Bohemica

Similarity:

In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form x ( t ) - c x ( t - r ) ’ P ( t ) x ( t - θ ) - Q ( t ) x ( t - δ ) =0 where c > 0 , r > 0 , θ > δ ≥ 0 are constants, and P , Q ∈ C ( ℝ + , ℝ + ) . We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient conditions for the existence of bounded and unbounded oscillatory solutions.