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Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations

Monika Sobalová — 2002

Archivum Mathematicum

In the paper the fourth order nonlinear differential equation y ( 4 ) + ( q ( t ) y ' ) ' + r ( t ) f ( y ) = 0 , where q C 1 ( [ 0 , ) ) , r C 0 ( [ 0 , ) ) , f C 0 ( R ) , r 0 and f ( x ) x > 0 for x 0 is considered. We investigate the asymptotic behaviour of nonoscillatory solutions and give sufficient conditions under which all nonoscillatory solutions either are unbounded or tend to zero for t .

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