Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 37, pp. 1-17.

Title: Existence of solutions for implicit obstacle problems involving nonhomogeneous
       partial differential operators and multivalued terms
       
Authors: Shengda Zeng (Yulin Normal Univ., Yulin, China)
         Yunru Bai (Guangxi Univ. of Science and Tech., Liuzhou, Guangxi, China)
         Leszek Gasinski (Pedagogical Univ. of Cracow, Poland)
         Ireneusz Krech  (Pedagogical Univ. of Cracow, Poland)

Abstract: 
 In 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.

Submitted April 1, 2020. Published May 06, 2021.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Implicit obstacle problem;  Clarke generalized gradient;
           nonhomogeneous partial differential operator; fixed point theorem; 
           surjectivity theorem.