On oscillatory behavior of solutions of second order functional differential equations
The author considers the following functional-differential equation (1) \((a(t) \psi (x(t)) x'(t))' + P(t,x(t), x'(t)) + Q(t,x[g(t)]) = e(t)\), where \(a,e : [t_ 0, \infty) \to [0, \infty)\), \(\psi:\mathbb{R}\to\mathbb{R}\), \(P : [t_ 0, \infty) \times\mathbb{R}\to\mathbb{R}\), \(Q : [t_ 0, \infty) \times\mathbb{R}\to\mathbb{R}\) are continuous, \(a(t) > 0\), \(g(t) \to \infty\) as \(t \to \infty\). In the paper the oscillatory and asymptotic behavior of solutions of (1) is discussed. The obtained results extend some of those in the literature.
scientific article; zbMATH DE number 637516