The impact of unbounded swings of the forcing term on the asymptotic behavior of functional equations.

*(English)*Zbl 1045.34051Summary: Necessary and sufficient conditions are obtained to force all solutions of the equation
\[
(r(t)y'(t))^{(n-1)} + a(t)h(y(g(t))) = f(t)
\]
to behave in peculiar ways. These results are then extended to the elliptic equation
\[
| x| ^{p-1} \Delta y(| x| ) + a(| x| )h(y(g(| x| ))) = f(| x| )
\]
where \( \Delta \) is the Laplace operator and \(p \geq 3\) is an integer.

##### MSC:

34K25 | Asymptotic theory of functional-differential equations |

35B40 | Asymptotic behavior of solutions to PDEs |

**OpenURL**

##### References:

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