Asymptotic shape of solutions to nonlinear eigenvalue problems
| dc.contributor.author | Shibata, Tetsutaro | |
| dc.date.accessioned | 2021-05-20T20:06:55Z | |
| dc.date.available | 2021-05-20T20:06:55Z | |
| dc.date.issued | 2005-03-29 | |
| dc.description.abstract | We consider the nonlinear eigenvalue problem -u''(t) = ƒ(λ, u(t)), u > 0, u(0) = u(1) =0, where λ > 0 is a parameter. It is known that under some conditions on ƒ(λ, u), the shape of the solutions associated with λ is almost 'box' when λ ≫ 1. The purpose of this paper is to study precisely the asymptotic shape of the solutions as λ → ∞ from a standpoint of L1-framework. To do this, we establish the asymptotic formulas for L<sup>1</sup>-norm of the solutions as λ → ∞. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 16 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Shibata, T. (2005). Asymptotic shape of solutions to nonlinear eigenvalue problems. <i>Electronic Journal of Differential Equations, 2005</i>(37), pp. 1-16. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13611 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Asymptotic formula | |
| dc.subject | L1-norm | |
| dc.subject | Simple pendulum | |
| dc.subject | Logistic equation | |
| dc.title | Asymptotic shape of solutions to nonlinear eigenvalue problems | |
| dc.type | Article |