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Fourth-order differential equation with deviating argument. (English) Zbl 1244.34089
Summary: We consider the fourth-order differential equation with middle-term and deviating argument \[ x^{(4)}(t) + q(t)x^{(2)}(t) + r(t)f(x(\varphi(t))) = 0 \] 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.

34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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