Oscillations of Difference Equations with Several Oscillating Coefficients

Abstract EN

We study the oscillatory behavior of the solutions of the difference equation Δx(n)+∑i=1mpi(n)x(τi(n))=0,n∈N0[∇xn-∑i=1mpinxσin=0, n∈N] where (pi(n)), 1≤i≤m are real sequences with oscillating terms, τi(n)[σi(n)], 1≤i≤m are general retarded (advanced) arguments, and Δ[∇] denotes the forward (backward) difference operator Δx(n)=x(n+1)-x(n)[∇x(n)=x(n)-x(n-1)].

Examples illustrating the results are also given.