Spectrum, global bifurcation and nodal solutions to Kirchhoff-type equations
| dc.contributor.author | Cao, Xiaofei | |
| dc.contributor.author | Dai, Guowei | |
| dc.date.accessioned | 2022-03-10T14:17:22Z | |
| dc.date.available | 2022-03-10T14:17:22Z | |
| dc.date.issued | 2018-11-05 | |
| dc.description.abstract | In this article, we consider a Dancer-type unilateral global bifurcation for the Kirchhoff-type problem -(α + b ∫1 0 |u′|2 dx)u″ = λu + h(x, u, λ) in (0, 1), u(0) = u(1) = 0. Under natural hypotheses on h, we show that (αλk, 0) is a bifurcation point of the above problem. As applications we determine the interval of λ, in which there exist nodal solutions for the Kirchhoff-type problem -(α + b ∫1 0 |u′|2 dx)u″ = λƒ(x, u) in (0, 1), u(0) = u(1) = 0, where ƒ is asymptotically linear at zero and is asymptotically 3-linear at infinity. To do this, we also establish a complete characterization of the spectrum of a nonlocal eigenvalue problem. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Cao, X., & Dai, G. (2018). Spectrum, global bifurcation and nodal solutions to Kirchhoff-type equations. Electronic Journal of Differential Equations, 2018(179), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15475 | |
| dc.language.iso | en | |
| dc.publisher | 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, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Bifurcation | |
| dc.subject | Spectrum | |
| dc.subject | Nonlocal problem | |
| dc.subject | Nodal solution | |
| dc.title | Spectrum, global bifurcation and nodal solutions to Kirchhoff-type equations | |
| dc.type | Article |