ABSTRACT
Abstract We deal with the nonlinear difference equation with deviating argument
∆ ( a(n)Φp(∆x(n))
) = b(n)f
( x(g(n))
) , Φp(u) = |u|p−2u p > 1,
where {a(n)}, {b(n)} are positive real sequences for n ≥ n0, f : [0,∞) → [0,∞) is continuous with f(0) = 0, f(u) > 0 for u > 0 and {g(n)} is a sequence of positive integers such that limn g(n) =∞. Necessary and sufficient conditions for the existence of positive solutions approaching zero are given. The role of the nonlinearity f and the effect of the deviating argument are enlightened and illustrated by examples.
