OSCILLATION CRITERIA FOR SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS

摘要

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 (r_1(t)(x(t) +p_1(t)x(τ(t)))')' + r_2(t)(x(t) +p_2(t)x(σ(t))' +p(t)G(x(α(t))) - q(t)H(x(β(t))) = 0 and (r_1 (t)(x(t) + p_1(t)x(τ(t)))')' + r_2(t)(x(t) + p_2(t)x(σ(t)))' +p(t)G(x(α(t))) - q(t)H(x(β(t))) = f(t) are studied for p_1(t),P_2(t) ∈ C([t_0,∞),?). Moreover, using Banach fixed point theorem, sufficient conditions are obtained for the existence of bounded positive solutions of the forced equation.