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Boundedness criteria for a class of second order nonlinear differential equations with delay

Daniel O. Adams, Mathew O. Omeike, Idowu A. Osinuga, Biodun S. Badmus (2023)

Mathematica Bohemica

We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a ( t ) x ' ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) and ( a ( t ) x ' ) ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) , where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results. This work...

Boundedness results of solutions to the equation x ′′′ + a ⁢ x ′′ + g ⁢ ( x ) ⁢ x ′ + h ⁢ ( x ) = p ⁢ ( t ) without the hypothesis h ⁢ ( x ) ⁢ sgn ⁢ x ≥ 0 f ⁢ o ⁢ r ⁢ | x | > R .

Ján Andres (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi h ⁢ ( x ) ⁢ sgn ⁢ x ≥ 0 f ⁢ o ⁢ r ...

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