Gene

Quantum mechanics

Fixed point

Fixed-point theorem

Pure mathematics

Obstacle problem

Biochemistry

Differential operator

Obstacle

Physics

Variational inequality

Mathematics

Political science

Transcription factor

Mathematical analysis

Repressor

Chemistry

Operator (biology)

Term (time)

Calculus of Variations and Partial Differential Equations

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.

Existence results for double phase implicit obstacle problems involving multivalued operators