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Global monotonicity and oscillation for second order differential equation

Authors:

M Bartu?ek M Cecchi Z Do?lá M Marini

Institution:

M. Bartu

ek, M. Cecchi, Z. Do scaron

lá and M. Marini

Abstract:

Oscillatory properties of the second order nonlinear equation

$\left( {r\left( t \right)x'} \right)^\prime + q\left( t \right)f\left( x \right) = 0$

are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.

Keywords:

second order nonlinear differential equation oscillatory solution nonoscillatory solution coexistence problem

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