Infinite Homoclinic Solutions of the Discrete Partial Mean Curvature Problem with Unbounded Potential

Yanshan Chen and Zhan Zhou
Additional contact information
Yanshan Chen: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Zhan Zhou: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Mathematics, 2022, vol. 10, issue 9, 1-12

Abstract: The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons. Under the assumptions that the potential function is unbounded and that the nonlinear term is superlinear at infinity, we obtain the existence of infinitely many homoclinic solutions to this problem by means of the fountain theorem in the critical point theory. In the end, an example is given to illustrate the applicability of our results.

Keywords: discrete partial mean curvature problem; homoclinic solution; unbounded potential; superlinearity; fountain theorem (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:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/9/1436/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/9/1436/ (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:9:p:1436-:d:801169

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 ().