Solution curves of 2m-th order boundary-value problems
| dc.contributor.author | Rynne, Bryan | |
| dc.date.accessioned | 2021-04-12T15:27:45Z | |
| dc.date.available | 2021-04-12T15:27:45Z | |
| dc.date.issued | 2004-03-03 | |
| dc.description.abstract | We consider a boundary-value problem of the form Lu = (λƒ (u), where L is a 2m-th order disconjugate ordinary differential operator (m ≥ 2 is an integer), λ ∈ [0, ∞), and the function ƒ : ℝ → ℝ is C2 and satisfies ƒ(ξ) > 0, ξ ∈ ℝ. Under various convexity or concavity type assumptions on ƒ we show that this problem has a smooth curve, S0, of solutions (λ, u), emanating from (λ, u) = (0, 0), and we describe the shape and asymptotes of S0. All the solutions on S0 are positive and all solutions for which u is stable lie on S0. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 16 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Rynne, B. P. (2004). Solution curves of 2m-th order boundary-value problems. <i>Electronic Journal of Differential Equations, 2004</i>(32), pp. 1-16. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13360 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Ordinary differential equations | |
| dc.subject | Nonlinear boundary value problems | |
| dc.title | Solution curves of 2m-th order boundary-value problems | |
| dc.type | Article |