... phenomena, for instance, in the theoryof 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 ... see, e.g., 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, ... to quasilinear problems whichare relevant in itself and will play a key role in the proof of Theorem 1.1.We begin with the problem of finding classical solutions for the differential inequality−Δpv...