Existence results for double phase implicit obstacle problems involving multivalued operators

By Shengda Zeng, Yunru Bai, Leszek Gasinski, Patrick Winkert. Calculus of Variations and Partial Differential Equations, 2020

131 citations recorded by the source corpus.

In this paper we study implicit obstacle problems driven by a nonhomogenous differential operator, called double phase operator, and a multivalued term which is described by Clarke’s generalized gradient. Based on a surjectivity theorem for multivalued mappings, Kluge’s fixed point principle and tools from nonsmooth analysis, we prove the existence of at least one solution.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6b04dfd01a871b8c92eb91543e842a49a66b57e0

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

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.”
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–”
On double phase Kirchhoff problems with singular nonlinearity (2021, background): “[35,36] (multivalued obstacle problems), and the references therein.”
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, methodology): “We refer to the papers of BahrouniRădulescu-Winkert [3] (Baouendi-Grushin operator), Colasuonno-Squassina [15] (double phase eigenvalue problems), Farkas-Winkert [31] (Finsler double phase problems), Gasiński-Papageorgiou [32] (locally Lipschitz right-hand sides), Gasiński-Winkert [34, 35] (convecti”
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.”