Quasilinear differential inclusions driven by degenerated \(p\)-Laplacian with weight

Dumitru Motreanu


The main result of the paper provides the existence of a solution to a quasilinear inclusion problem with Dirichlet boundary condition which exhibits a term with full dependence on the solution and its gradient (convection term) and is driven by the degenerated \(p\)-Laplacian with weight. The multivalued term in the differential inclusion is in form of the generalized gradient of a locally Lipschitz function expressed through the primitive of a locally essentially bounded function, which makes the problem to be of a hemivariational inequality type. The novelty of our result is that we are able to simultaneously handle three major features: degenerated leading operator, convection term and discontinuous nonlinearity. Results of independent interest regard certain nonlinear operators associated to the differential inclusion.


differential inclusion; hemivariational inequality; quasilinear elliptic equation; degenerated \(p\)-Laplacian with weight; Dirichlet problem; convection; pseudomonotone operator

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DOI: http://dx.doi.org/10.24193/subbmath.2023.1.06


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