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

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.

Keywords

• Oscillation
• neutral differential equation
• second order
• distributed deviating argument
• Riccati technique.