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dc.contributor.authorCao, Xiaofei ( )
dc.contributor.authorDai, Guowei ( )
dc.date.accessioned2022-03-10T14:17:22Z
dc.date.available2022-03-10T14:17:22Z
dc.date.issued2018-11-05
dc.identifier.citationCao, X., & Dai, G. (2018). Spectrum, global bifurcation and nodal solutions to Kirchhoff-type equations. Electronic Journal of Differential Equations, 2018(179), pp. 1-10.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15475
dc.description.abstract

In this article, we consider a Dancer-type unilateral global bifurcation for the Kirchhoff-type problem

-(α + b ∫10 |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 ∫10 |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.formatText
dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectBifurcationen_US
dc.subjectSpectrumen_US
dc.subjectNonlocal problemen_US
dc.subjectNodal solutionen_US
dc.titleSpectrum, global bifurcation and nodal solutions to Kirchhoff-type equationsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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