Fourth-order differential equation with deviating argument (Q417096)
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scientific article; zbMATH DE number 6034186
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fourth-order differential equation with deviating argument |
scientific article; zbMATH DE number 6034186 |
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Fourth-order differential equation with deviating argument (English)
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14 May 2012
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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.
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