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The impact of unbounded swings of the forcing term on the asymptotic behavior of functional equations. (English) Zbl 1045.34051
Summary: 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
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References:
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