Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations

Lin-Lin Wang, Jing-Jing Liu and Yong-Hong Fan ()
Additional contact information
Lin-Lin Wang: School of Mathematics and Statistics Sciences, Ludong University, Yantai 264025, China
Jing-Jing Liu: School of Mathematics and Statistics Sciences, Ludong University, Yantai 264025, China
Yong-Hong Fan: School of Mathematics and Statistics Sciences, Ludong University, Yantai 264025, China

Mathematics, 2024, vol. 12, issue 22, 1-14

Abstract: A class of semilinear elliptic differential equations was investigated in this study. By constructing the inverse function, using the method of upper and lower solutions and the principle of comparison, the existence of the maximum positive solution and the minimum positive solution was explored. Furthermore, the uniqueness of the positive solution and its asymptotic estimation at the origin were evaluated. The results show that the asymptotic estimation is similar to that of the corresponding boundary blowup problems. Compared with the conclusions of Wei’s work in 2017, the asymptotic behavior of the solution only depends on the asymptotic behavior of b ( x ) at the origin and the asymptotic behavior of g at infinity.

Keywords: semilinear elliptic differential equation; upper and lower solution; blowup problem; uniqueness; asymptotic behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/22/3624/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/22/3624/ (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:12:y:2024:i:22:p:3624-:d:1525122

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 ().