Oscillation criteria for nonlinear second order differential equations with damping. (English) Zbl 1105.34019

Summary: Using the integral average method, we give some new oscillation criteria for the second-order differential equation with a damping term \[ (a(t)\Psi(x(t))K(x'(t)))'+p(t)K(x'(t))+q(t)f(x(t))=0,\quad t \leq t_0. \] These results improve and generalize the oscillation criteria in the work of B. Ayanlar and A. Tiryaki [Acta Math. Hungar. 89, 1–13 (2000; Zbl 0973.34021)], because they eliminate both the differentiability of \(p(t)\) and the sign of \(p(t)\), \(q(t)\). As a consequence, improvements of Sobol-type oscillation criteria are obtained.


34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations


Zbl 0973.34021
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