Optimal problem of cost function for the linear neutral systems.
In this paper, oscillattion and nonoscillation criteria are established for neutral differential equations with positive and negative coefficients. Our criteria improve and extend many results known in the literature.
Our aim in this paper is to present sufficient conditions for the oscillation of the second order neutral differential equation (x(t)-px(t-))"+q(t)x((t))=0.
2000 Mathematics Subject Classification: 39A10.The oscillatory and nonoscillatory behaviour of solutions of the second order quasi linear neutral delay difference equation Δ(an | Δ(xn+pnxn-τ)|α-1 Δ(xn+pnxn-τ) + qnf(xn-σ)g(Δxn) = 0 where n ∈ N(n0), α > 0, τ, σ are fixed non negative integers, {an}, {pn}, {qn} are real sequences and f and g real valued continuous functions are studied. Our results generalize and improve some known results of neutral delay difference equations.