On some differential inclusions with anti-periodic solutions

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 ( , ( , and ( ), involve operators that are odd, maximal monotone, and pos...

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Published inAnalele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică Vol. 33; no. 2; pp. 157 - 178
Main Author Vîntu, Ioan Vladimir
Format Journal Article
LanguageEnglish
Published Constanta Sciendo 01.06.2025
De Gruyter Poland
Subjects
anti-periodic solution
Evolution inclusion
maximal monotone operator
Primary 34G25, 47J35, 47H05
Secondary 35L40
telegraph system
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Summary: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 ( , ( , and ( ), involve operators that are odd, maximal monotone, and possibly set-valued. The second- and first-order differential inclusions are parameterized by two nonnegative constants, and , which affect the behavior of the differential terms. We establish the existence and uniqueness of strong solutions for the problems ( and ( , as well as for the algebraic inclusion ( ). Additionally, we prove the continuous dependence of the solution to problem ( on parameters ɛ and We also provide approximation results for the solutions to ( and ( ) as the parameters and approach zero. Finally, we discuss some applications of our theoretical results.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1224-1784
1844-0835
DOI:10.2478/auom-2025-0024