Quasilinear differential inclusions driven by degenerated p-Laplacian with weight
DOI:
https://doi.org/10.24193/subbmath.2023.1.06Keywords:
Differential inclusion, hemivariational inequality, quasilinear elliptic equation, degenerated p-Laplacian with weight, Dirichlet problem, convection, pseudomonotone operator.Abstract
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.
Mathematics Subject Classification (2010): 35J87, 35J62, 35J70.
Received 13 September 2022; Revised 21 January 2023. Published Online: 2023-03-20. Published Print: 2023-04-30
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