Existence of solutions for a class of nonlocal p ( b ( u ) ) & q ( b ( u ) ) elliptic problems

In this work, we consider the following nonlocal quasilinear elliptic problem − M ( A ( u ) ) div ⁡ ( a ( | ∇ u | p ( b ( u ) ) ) | ∇ u | p ( b ( u ) ) − 2 ∇ u ) = f ( x , u ) , with a homogeneous Dirichlet boundary condition. Under suitable conditions on the functions M , a , p , b and f employing an approximation method combined with fixed point arguments, we obtain the existence of a weak solution for the above problem.