Precise Asymptotics for Bifurcation Curve of Nonlinear Ordinary Differential Equation

Tetsutaro Shibata
Additional contact information
Tetsutaro Shibata: Laboratory of Mathematics, School of Engineering, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

Mathematics, 2020, vol. 8, issue 8, 1-15

Abstract: We study the following nonlinear eigenvalue problem − u ″ ( t ) = λ f ( u ( t ) ) , u ( t ) > 0 , t ∈ I : = ( − 1 , 1 ) , u ( ± 1 ) = 0 , where f ( u ) = log ( 1 + u ) and λ > 0 is a parameter. Then λ is a continuous function of α > 0 , where α is the maximum norm α = ? u λ ? ∞ of the solution u λ associated with λ . We establish the precise asymptotic formula for λ = λ ( α ) as α → ∞ up to the third term of λ ( α ) .

Keywords: precese asymptotics; global bifurcation; time-map argument (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/8/1272/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/8/1272/ (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:8:y:2020:i:8:p:1272-:d:393791

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 ().