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Further results for some third order differential systems with nonlinear dissipation

Awar Simon Ukpera — 2004

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We formulate nonuniform nonresonance criteria for certain third order differential systems of the form X ' ' ' + A X ' ' + G ( t , X ' ) + C X = P ( t ) , which further improves upon our recent results in [12], given under sharp nonresonance considerations. The work also provides extensions and generalisations to the results of Ezeilo and Omari [5], and Minhós [9] from the scalar to the vector situations.

Results on Non-resonant Oscillations for some Nonlinear Vector Fourth Order Differential Systems

Awar Simon Ukpera;  Olufemi Adeyinka Adesina — 2012

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper presents vector versions of some existence results recently published for certain fourth order differential systems based on generalisations drawn from possibilities arising from the underlying auxiliary equation. The results obtained also extend some known works involving third order differential systems to the corresponding fourth order.

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