Zafer AĞACIK, Aydın TİRYAKİ

4980

Oscillation Criteria for Second Order Nonlinear Differential Equations with Damping

Oscillation criteria are given for second order nonlinear differential equations with damping of the form (a(t) y (x ) \dot x)\dot{}+ p(t) \dot x + q (t) f (x ) = 0,\quad t\geq t0, where p and q are allowed to change signs on [t0,\infty). We employ the averaging technique to obtain sufficient conditions for oscillation of solutions of the above equation. Our results generalize and extend some known oscillation criteria in the literature.

Anahtar Kelimeler:

Oscillation, averaging, damping, Riccati substitution, second order.

Oscillation Criteria for Second Order Nonlinear Differential Equations with Damping

Oscillation criteria are given for second order nonlinear differential equations with damping of the form (a(t) y (x ) \dot x)\dot{}+ p(t) \dot x + q (t) f (x ) = 0,\quad t\geq t0, where p and q are allowed to change signs on [t0,\infty). We employ the averaging technique to obtain sufficient conditions for oscillation of solutions of the above equation. Our results generalize and extend some known oscillation criteria in the literature.

Keywords:

Oscillation, averaging, damping, Riccati substitution, second order.,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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Oscillation Criteria for Second Order Nonlinear Differential Equations with Damping

Zafer AĞACIK, Aydın TİRYAKİ