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Oscillation criteria for second order nonlinear neutral differential equations. (English) Zbl 1195.34098

The paper deals with the oscillatory behavior of second order nonlinear neutral delay differential equations of the form

(r(t)(x(t)+p(t)x(t-τ)) ' ) ' +q(t)f(x(t),x(σ(t)))=0,(1)

where tt 0 >0, τ0 is a constant, and moreover r,σC 1 ([t 0 ,),(0,)), p,qC([t 0 ,),), and fC( 2 ,). The purpose of the paper is to improve oscillation results obtained for equation (1) by W. Shi and P. Wang [Appl. Math. Comput. 146, No. 1, 211–226 (2003; Zbl 1037.34059)] using a generalized Riccati transformation and developing ideas exploited by Yu. V. Rogovchenko and F. Tuncay [Nonlinear Anal., Theory Methods Appl. 69, No. 1 (A), 208–221 (2008; Zbl 1147.34026)]. Two examples are provided to illustrate the relevance of obtained results.

MSC:
34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
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