“…See, in this regard, Shahrouzi. 7,8 On the other hand, it is known that modeling of some physical phenomena such as flows of electro-rheological fluids, nonlinear viscoelasticity, and image processing gives rise to equation with nonstandard growth conditions, that is, equations with variable exponents of nonlinearities. In direct problems, equations with nonlinearities of variable-exponent type have largely been discussed by several authors.…”