Asymptotic and oscillatory behavior of a class of second order functional differential equations
Oscillation theorems are proved for functional-differential equations of the type \[ (1)\quad -(r(t)g(x(t))x'(t))'=\quad p(t)x'(t)+q(t)f(x[\phi (t)]),\quad t\geq t_ 0 \] under suitable conditions on the functions f,g,p,q,r,\(\phi\). In particular, q(t) is allowed to change sign in \([t_ 0,\infty)\) and \(\phi\) (t) can be of retarded or advanced type. One theorem gives sufficient conditions for every solution x(t) of (1) to be either oscillatory at \(\infty\) or to decay monotonely to zero as \(t\to \infty\).
scientific article; zbMATH DE number 4198520
scientific article