Integral Averaging Techniques for Oscillation of Second Order Nonlinear DifferentialEquations With Damping

Jelena V. Manojlovi\'c

Abstract: New oscillation criteria are established for the second order nonlinear differential equation with a damping term $$ [a(t)\psi(x(t))x'(t)]'+p(t)x'(t)+q(t)f(x(t))=0. $$ These criteria are obtained by using an integral averaging technique. Moreover, we give conditions which ensure that every solution $x(t)$ of the forced second order differential equation with a damping term $$ [a(t)\psi(x(t))x'(t)]'+p(t)x'(t)+q(t)f(x(t))=r(t) $$ satisfies $\liminf_{t\to\infty} |x(t)|=0$.

Keywords: Oscillation, Nonlinear differential equations, Integral averages

Classification (MSC2000): 34C10; 34C15

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