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Integral averaging techniques for the oscillation of second order nonlinear differential equations. (English) Zbl 0697.34040

Summary: We enlist some known and establish some new oscillation criteria for the second order nonlinear differential equations of the form \[ (a(t)\psi (x(t))\dot x(t))^.+p(t)\dot x(t)+q(t)f(x(t))=0, \] where the coefficients p(t) and q(t) are not assumed to be nonnegative for all large values of t. These criteria are obtained by using integral averaging techniques and can be applied to some special cases where other classical oscillation results are not applicable. A systematic study is attempted to extend, improve, and correlate a number of existing results.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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