Gronwall’s lemmaIf, for t0≤t≤t1, ϕ(t)≥0 and ψ(t)≥0 are continuous functions such that the inequalityϕ(t)≤K+L∫t0tψ(s)ϕ(s)𝑑sholds on t0≤t≤t1, with K and L positive constants, thenϕ(t)≤Kexp(L∫t0tψ(s)𝑑s)on t0≤t≤t1.