oscillation criteria for second-order neutral differential equations with distributed deviating arguments

oscillation criteria for second-order neutral differential equations with distributed deviating arguments

;Gaihua Gui;Zhiting Xu
icsoft 2006 - 1st international conference on software and data technologies, proceedings 2007 Vol. 2007 pp. 1-11
180
gui2007electronicoscillation

Abstract

Using a class of test functions $Phi(t,s,T)$ defined by Sun [13] and a generalized Riccati technique, we establish some new oscillation criteria for the second-order neutral differential equation with distributed deviating argument $$ (r(t)psi(x(t))Z'(t))'+int^b_a q(t,xi)f[x(g(t,xi))]dsigma(xi)=0,quad tgeq t_0, $$ where $Z(t)=x(t)+p(t)x(t-au)$. The obtained results are different from most known ones and can be applied to many cases which are not covered by existing results.

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