Fourth-Order Differential Equation with Deviating Argument

الملخص EN

We consider the fourth-order differential equation with middle-term and deviating argument x(4)(t)+q(t)x(2)(t)+r(t)f(x(φ(t)))=0, in case when the corresponding second-order equation h″+q(t)h=0 is oscillatory.

Necessary and sufficient conditions for the existence of bounded and unbounded asymptotically linear solutions are given.

The roles of the deviating argument and the nonlinearity are explained, too.