Zeng, ShengdaBai, YunruGasinski, LeszekKrech, Ireneusz2021-08-262021-08-262021-05-06Zeng, S., Bai, Y., Gasinski, L., & Krech, I. (2021). Existence of solutions for implicit obstacle problems involving nonhomogeneous partial differential operators and multivalued terms. <i>Electronic Journal of Differential Equations, 2021</i>(37), pp. 1-18.1072-6691https://hdl.handle.net/10877/14447In this article, we study an implicit obstacle problem with a nonlinear nonhomogeneous partial differential operator and a multivalued operator which is described by a generalized gradient. Under quite general assumptions on the data, and employing Kluge's fixed point principle for multivalued operators, Minty technique and a surjectivity theorem, we prove that the set of weak solutions to the problem is nonempty, bounded and weakly closed.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalImplicit obstacle problemClarke generalized gradientNonhomogeneous partial differential operatorFixed point theoremSurjectivity theoremArticle