Global structure of solutions to boundary-value problems of impulsive differential equations
| dc.contributor.author | Niu, Yanmin | |
| dc.contributor.author | Yan, Baoqiang | |
| dc.date.accessioned | 2023-06-14T19:00:01Z | |
| dc.date.available | 2023-06-14T19:00:01Z | |
| dc.date.issued | 2016-02-25 | |
| dc.description.abstract | In this article, we study the structure of global solutions to the boundary-value problem -x″(t) + ƒ(t, x) = λαx(t), t ∈ (0, 1), t ≠ 1/2, ∆x|t=1/2 = β1x(1/2), ∆x′|t=1/2 = -β2x(1/2), x(0) = x(1) = 0, where λ ≠ 0, β1 ≥ β2 ≥ 0, ∆x|t=1/2 = x(1/2 + 0) - x(1/2), ∆x′|t=1/2 = x′(1/2 + 0) - x′(1/2 - 0), and ƒ : [0, 1] x ℝ → ℝ, α : [0, 1] → (0, +∞) are continuous. By a comparison principle and spectral properties of the corresponding linear equations, we prove the existence of solutions by using Rabinowitz-type global bifurcation theorems, and obtain results on the behavior of positive solutions for large λ where ƒ(x) = xp+1. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 23 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Niu, Y., & Yan, B. (2016). Global structure of solutions to boundary-value problems of impulsive differential equations. Electronic Journal of Differential Equations, 2016(55), pp. 1-23. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16929 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, 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, 2016, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Comparison arguments | |
| dc.subject | Eigenvalues | |
| dc.subject | Global bifurcation theorem | |
| dc.subject | Multiple solutions | |
| dc.subject | Asymptotical behavior of solutions | |
| dc.title | Global structure of solutions to boundary-value problems of impulsive differential equations | |
| dc.type | Article |