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.
MSC:
| 34K12 | Growth, boundedness, comparison of solutions to functional-differential equations |
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