On the oscillation of certain functional differential equations
The equation \(x^{(n)}(t)+ p(t) x^{(n- 1)}(t- h)= H(t, x(g(t)))\), \(n\geq 2\), is considered, where \(p: \mathbb{R}_+\to \mathbb{R}_+\), \(g: \mathbb{R}_+\to \mathbb{R}\), \(H: \mathbb{R}_+\times \mathbb{R}\to \mathbb{R}\) are continuous functions, \(h\in ]0, +\infty[\), \(\lim_{t\to + \infty} g(t)= +\infty\). Sufficient conditions are given for every solution of this equation to be oscillatory when \(n\) is even, and either to be oscillatory or satisfy \(x^{(i)}(t)\to 0\) monotonically as \(t\to +\infty\) \((i= 0, \dots, n- 2)\) when \(n\) is odd.
scientific article; zbMATH DE number 811236