Oscillation criteria for second order neutral differential equations with positive and negative coefficients

Abstract

In this paper oscillatory and asymptotic behavior of solutions of a class of nonlinear second order neutral differential equations with positive and negative coefficients of the form (r1(t)(x(t) + p1(t)x(τ(t)))′) ′+ r2(t)(x(t) + p2(t)x(σ(t)))′+p(t)G(x(α(t)))-q(t)H(x(β(t))) = 0 and (r1(t)(x(t) + p1(t)x(τ(t))) ′) ′+ r2(t)(x(t) + p2(t)x(σ(t))) ′+p(t)G(x(α(t)))-q(t)H(x(β(t))) = f(t) are studied for p1(t); p2(t) ∈ C([t0;∞);ℝ). Moreover, using Banach fixed point theorem, sufficient conditions are obtained for the existence of bounded positive solutions of the forced equation.