Existence of positive solutions for a neutral differential equation with positive and negative coefficients

This work is concerned with the existence of positive solutions for the neutral delay differential equation with positive and negative coefficients [x(t)−R(t)x(t−r)]′+P(t)x(t−τ)−Q(t)x(t−σ)=0,[x(t)−R(t)x(t−r)]′+P(t)x(t−τ)−Q(t)x(t−σ)=0, where P,Q,R∈C([t0,∞),R+),r>0,τ≥σ≥0P,Q,R∈C([t0,∞),R+),r>0,τ≥σ≥0.