Displaying similar documents to “Asymptotic behavior of solutions of neutral nonlinear differential equations”

On Existence and Asymptotic Properties of Kneser Solutions to Singular Second Order ODE.

Jana Vampolová (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We investigate an asymptotic behaviour of damped non-oscillatory solutions of the initial value problem with a time singularity p ( t ) u ' ( t ) ' + p ( t ) f ( u ( t ) ) = 0 , u ( 0 ) = u 0 , u ' ( 0 ) = 0 on the unbounded domain [ 0 , ) . Function f is locally Lipschitz continuous on and has at least three zeros L 0 < 0 , 0 and L > 0 . The initial value u 0 ( L 0 , L ) { 0 } . Function p is continuous on [ 0 , ) , has a positive continuous derivative on ( 0 , ) and p ( 0 ) = 0 . Asymptotic formulas for damped non-oscillatory solutions and their first derivatives are derived under some additional assumptions. Further,...

Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations

Monika Sobalová (2002)

Archivum Mathematicum

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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 .

Nonoscillation and asymptotic behaviour for third order nonlinear differential equations

Aydın Tiryaki, A. Okay Çelebi (1998)

Czechoslovak Mathematical Journal

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In this paper we consider the equation y ' ' ' + q ( t ) y ' α + p ( t ) h ( y ) = 0 , where p , q are real valued continuous functions on [ 0 , ) such that q ( t ) 0 , p ( t ) 0 and h ( y ) is continuous in ( - , ) such that h ( y ) y > 0 for y 0 . We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.

On asymptotic decaying solutions for a class of second order differential equations

Serena Matucci (1999)

Archivum Mathematicum

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The author considers the quasilinear differential equations r ( t ) ϕ ( x ' ) ' + q ( t ) f ( x ) = 0 , t a and r ( t ) ϕ ( x ' ) ' + F ( t , x ) = ± g ( t ) , t a . By means of topological tools there are established conditions ensuring the existence of nonnegative asymptotic decaying solutions of these equations.