Existence of solutions for double phase obstacle problems with multivalued convection term

By Shengda Zeng, Leszek Gasinski, Patrick Winkert, Yunru Bai. Journal of Mathematical Analysis and Applications, 2020

60 citations recorded by the source corpus.

Abstract The main goal of this paper is the study of an elliptic obstacle problem with a double phase phenomena and a multivalued reaction term which also depends on the gradient of the solution. Such term is called multivalued convection term. Under quite general assumptions on the data, we prove that the set of weak solutions to our problem is nonempty, bounded and closed. Our proof is based on a surjectivity theorem for multivalued mappings generated by the sum of a maximal monotone multivalued operator and a bounded multivalued pseudomonotone mapping.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/06c99bf94987b4e7dc225aea7d6ee5642cd22d62

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, unknown): “We refer to Bahrouni-Rădulescu-Winkert [3], Cencelj-RădulescuRepovš [12], Marino-Winkert [29], Papageorgiou-Rădulescu-Repovš [35], [36], [37], Rădulescu [42], Zhang-Rădulescu [48], Zeng-Gasiński-Winkert-Bai [46], [47] and the references therein.”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “Estimates of the Calderón-Zygmund type can be extended to obstacle problems, too (see [42,154]); in that case various existence results are also available [213].”
On double phase Kirchhoff problems with singular nonlinearity (2021, background): “[35,36] (multivalued obstacle problems), and the references therein.”
Existence of solutions for singular double phase problems via the Nehari manifold method (2021, background): “Finally, existence results for double phase problems with homogeneous Dirichlet or nonlinear Neumann boundary conditions without singular term can be found in the papers of Colasuonno–Squassina [13], El Manouni–Marino–Winkert [22], Gasiński–Papageorgiou [26], Gasiński–Winkert [28–30], Liu–Dai [34–”
An existence result for singular Finsler double phase problems (2020, methodology): “We refer to the works of Bahrouni-Rădulescu-Winkert [1], Marino-Winkert [33], Papageorgiou-Rădulescu-Repovš [37], Papageorgiou-Winkert [39,40], Zeng-Bai-Gasiński-Winkert [48,47] and the references therein.”