Spectrum of Discrete Second-Order Difference Operator with Sign-Changing Weight and Its Applications

Abstract EN

Let T>1 be an integer, and let?=1,2,…,T.

We discuss the spectrum of discrete linear second-order eigenvalue problems Δ2ut-1+λmtut=0, t∈?, u0=uT+1=0, where λ≠0 is a parameter, m:?→ℝ changes sign and mt≠0 on ?.

At last, as an application of this spectrum result, we show the existence of sign-changing solutions of discrete nonlinear second-order problems by using bifurcate technique.