On some differential inclusions with anti-periodic solutions

Abstract

In this paper, we investigate a class of second- and first-order differential inclusions, along with an algebraic inclusion, all subject to anti-periodic boundary conditions in a real Hilbert space. These problems, denoted as (Pɛμ)ap, (Pµ)ap, and (E00), involve operators that are odd, maximal monotone, and possibly set-valued. The second- and first-order differential inclusions are parameterized by two nonnegative constants, ɛ and µ, which affect the behavior of the differential terms.

Keywords

• evolution inclusion
• anti-periodic solution
• maximal monotone operator
• telegraph system
• primary 34g25, 47j35, 47h05
• secondary 35l40