Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball

Valery Karachik, Batirkhan Turmetov and Hongfen Yuan
Additional contact information
Valery Karachik: Department of Mathematical Analysis, South Ural State University (NRU), 454080 Chelyabinsk, Russia
Batirkhan Turmetov: Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan
Hongfen Yuan: School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China

Mathematics, 2022, vol. 10, issue 7, 1-21

Abstract: Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier–Neumann boundary value problems are studied. For the problems under consideration, existence and uniqueness theorems are proved. Necessary and sufficient conditions for the solvability of all problems are obtained and an integral representations of solutions are given in terms of the corresponding Green’s functions.

Keywords: nonlocal equation; biharmonic equation; Dirichlet problem; Neumann problem; Navier problem; Riquier–Neumann problem; existence and uniqueness; Green’s function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/7/1158/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/7/1158/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:7:p:1158-:d:786355

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().