Differential inclusion problems with convolution and discontinuous nonlinearities

The paper investigates a new type of differential inclusion problem driven by a weighted (p, q)-Laplacian and subject to Dirichlet boundary condition. The problem fully depends on the solution and its gradient. The main novelty is that the problem exhibits simultaneously a nonlocal term involving convolution with the solution and a multivalued term describing discontinuous nonlinearities for the solution. Results stating existence, uniqueness and dependence on parameters are established.