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

Authors:

Institution:

(1) Department of Mathematics, University of Wisconsin Centers, Manitowoc County, 705 Viebahn St., Manitowoc, WI, 54220, U.S.A.

Abstract:

Necessary and sufficient conditions have been found to force all solutions of the equation

$(r(t)y'{\text{(}}t{\text{))}}^{{\text{(}}n - 1{\text{)}}} + a(t)h(y(g(t))) = f(t),$

to behave in peculiar ways. These results are then extended to the elliptic equation

${\text{|}}x{\text{|}}^{p - 1} \Delta y{\text{(|}}x{\text{|) + }}a{\text{(|}}x{\text{|)}}h(y(g{\text{(|}}x{\text{|)))}} = f{\text{(|}}x{\text{|)}}$

where

is the Laplace operator and p

3 is an integer.

Keywords:

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