Fourth-Order Differential Equation with Deviating Argument. (18th March 2012) - Bartušek, M.; Cecchi, M.; Došlá, Z.; Marini, M.
Abstract : 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.