... phenomena, for instance, in the theory of quasiregular and quasiconformal mappings 1–3, in the generalized reaction-diffusiontheory 4, in the turbulent flow of a gas in porous medium and in the non-Newtonianfluid ... this, the inequality 1.4 is a consequence of a result in 6. This completes the proof of Theorem 1.1.AppendixProof of Lemma 2.4. The proof of item iv is an immediate consequence of Lemma ... 8–20 and references therein for more generalnonlinearities in the terms f and g which include the cases considered by them. The principal theorem in 7 considered, in problem 1.1, fuum,u>0,...