Existence of nonoscillatory and oscillatory solutions to neutral differential equations with positive and negative coefficients. (English) Zbl 0937.34066

Graef, John R.; Yang, Bo; Zhang, B. G.

Math. Bohem. 124, No. 1, 87-102 (1999).

Summary: The authors study the existence of oscillatory and nonoscillatory solutions to neutral differential equations of the form \[ (x(t)-cx(t-r))'\pm (P(t)x(t-\theta)-Q(t)x(t-\delta))=0 \] where \(c>0\), \(r>0\), \(\theta >\delta \geq 0\) are constants, and \(P\), \(Q\in C(\mathbb R^+ ,\mathbb R^+)\). They obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, and some sufficient conditions for the existence of bounded and unbounded oscillatory solutions.

MSC:

34K40	Neutral functional-differential equations
34K11	Oscillation theory of functional-differential equations

Keywords:

neutral differential equations; nonoscillation; oscillation; positive and negative coefficients