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 (r1(t)(x(t)+p1(t)x(τ(t)))')' + r2(t)(x(t)+P2(t)x(σ(t))' +p(t)G(x(a(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(a(t))) - q(t)H(x(β(t))) = f(t) are studied for p1(t), P2(t) ∈ C([to, ∞), R). Moreover, using Banach fixed point theorem, sufficient conditions are obtained for the existence of bounded positive solutions of the forced equation.