Positive solutions for singular discrete boundary value problems

Abstract

We study the existence of zero-convergent solutions for the second-order nonlinear difference equation Δ(anΦp(Δxn))=g(n,xn+1), where Φp(u)=|u|p−2u, p>1,{an} is a positive real sequence for n≥1, and g is a positive continuous function on ℕ×(0,u0), 0<u0≤∞. The effects of singular nonlinearities and of the forcing term are treated as well.