... limt→0ϕ(σt)ψ(t)= σp−1, for all σ ∈ R+, for some p > 1.(Φ2) lim|t|→∞ϕ(σt)ψ(t)= σq−1, for all σ ∈ R+, for some q > 1.(F1) f(t, u, λ) = ◦(|ψ(u)|) near zero, uniformly for t and λ in bounded ... ϕ4(σ).Moreover, f satisfies f(t, u, λ) = ◦(|ψ(u)|) near zero and infinity, uniformly in t and λ, anduf(t, u, λ) ≥ 0. Therefore, all hypotheses of Theorem 1.1 are satisfied.Example 4.2. Define ϕ, ... =t0−λnψ(un(ξ)) − f(ξ, un, λn)dξ. Since f(t, u, λ) = ◦(|ψ(u)|) near zero,uniformly for t and λ, for some constants K1and K2.∥dn∥0= maxt∈[0,1]|t0λnψ(un(ξ)) + f(ξ, un, λn)dξ|≤...