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

Bhagat Singh — 2000

Czechoslovak Mathematical Journal

Necessary and sufficient conditions have been found 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 Δ y ( | x | ) + a ( | x | ) h ( y ( g ( | x | ) ) ) = f ( | x | ) where Δ is the Laplace operator and p 3 is an integer.

On nonoscillation of canonical or noncanonical disconjugate functional equations

Bhagat Singh — 2000

Czechoslovak Mathematical Journal

Qualitative comparison of the nonoscillatory behavior of the equations L n y ( t ) + H ( t , y ( t ) ) = 0 and L n y ( t ) + H ( t , y ( g ( t ) ) ) = 0 is sought by way of finding different nonoscillation criteria for the above equations. L n is a disconjugate operator of the form L n = 1 p n ( t ) d d t 1 p n - 1 ( t ) d d t ... d d t · p 0 ( t ) . Both canonical and noncanonical forms of L n have been studied.

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