If the kernelKof equation (E) satisfies some additional conditions, then from Theorem3.1we can obtain many interesting results. Some of them are presented below.
Corollary 7.1. Assume x∈Sol(E)is(f,σ)-ordinary, y∈∆−mb is f -regular,
Corollary 7.5. Assume f(n,t) =et, s∈[1,∞), exists a solution x of (E)such that
xn= ϕ(n) +o(λn).
Proof. Note that
K∗(n) =n n
n+1 n2
, n
q
K∗(n) = √n n
n n+1
n
→ 1 e <λ, bn+1
bn = n
n+1 n
→ 1 e <λ.
HenceK0 ∈o(λn)andb∈o(λn). Moreover,ϕis f-regular and o(λn)is an evanescentm-space.
Therefore, the assertion follows from Corollary4.11.
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