Oscillation Criteria for Second Order Nonlinear Differential Equations with Damping

Authors : Aydin TİRYAKİ

Pages : 185-196

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Oscillation criteria are given for second order nonlinear differential equations with damping of the form insert ignore into journalissuearticles values(ainsert ignore into journalissuearticles values(t); y insert ignore into journalissuearticles values(x ); \dot x);\dot{}+ pinsert ignore into journalissuearticles values(t); \dot x + q insert ignore into journalissuearticles values(t); f insert ignore into journalissuearticles values(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