Nonstandard Dirichlet problems with competing (p, q)-Laplacian, convection, and convolution

The paper focuses on a nonstandard Dirichlet problem driven by the operator -Delta(p) + mu Delta(q) which is a competing (p, q)-Laplacian with lack of ellipticity if mu > 0, and exhibiting a reaction term in the form of a convection (i.e., it depends on the solution and its gradient) composed with the convolution of the solution with an integrable function. We prove the existence of a generalized solution through a combination of fixed-point approach and approximation. In the case mu <= 0, we obtain the existence of a weak solution to the respective elliptic problem.