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Differential inclusion problems with convolution and discontinuous nonlinearities

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  • 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.

    Mathematics Subject Classification: Primary: 35J92, 35J87; Secondary: 49J52.

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