Abstract
AbstractIn this paper, a nonlinear elliptic obstacle problem is studied. The nonlinear nonhomogeneous partial differential operator generalizes the notions of p-Laplacian while on the right hand side we have a multivalued convection term (i.e., a multivalued reaction term may depend also on the gradient of the solution). The main result of the paper provides existence of the solutions as well as bondedness and closedness of the set of weak solutions of the problem, under quite general assumptions on the data. The main tool of the paper is the surjectivity theorem for multivalued functions given by the sum of a maximal monotone multivalued operator and a bounded multivalued pseudomonotone one.
Funder
NNSF of China Grant
European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement
National Science Center of Poland under Preludium Project
Publisher
Springer Science and Business Media LLC
Reference32 articles.
1. Averna, D., Motreanu, D., Tornatore, E.: Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence. Appl. Math. Lett. 61, 102–107 (2016)
2. Bai, Y.R.: Existence of solutions to nonhomogeneous Dirichlet problems with dependence on the gradient. Electron. J. Differ. Equ. 101(18), (2018) pp. 1–18
3. Bai, Y.R., Gasiński, L., Papageorgiou, N.S.: Nonlinear nonhomogeneous Robin problems with dependence on the gradient. Bound Value Probl. 17, (2018). https://doi.org/10.1186/s13661-018-0936-8
4. Faraci, F., Motreanu, D., Puglisi, D.: Positive solutions of quasi-linear elliptic equations with dependence on the gradient. Cal. Var. PDEs 54(1), 525–538 (2015)
5. Gasiński, L., Papageorgiou, N.S.: On nonlinear elliptic hemivariational inequalities of second order. Acta Math. Sci. Ser. B (Engl. Ed.) 24(3), 451–462 (2004)
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