Electron. J. Differential Equations,
Vol. 2018 (2018), No. 179, pp. 110.
Spectrum, global bifurcation and nodal solutions to Kirchhofftype equations
Xiaofei Cao, Guowei Dai
Abstract:
In this article, we consider a Dancertype unilateral global bifurcation
for the Kirchhofftype problem
Under natural hypotheses on h, we show that
is a
bifurcation point of the above problem.
As applications we determine the interval of
,
in which there
exist nodal solutions for the Kirchhofftype problem
where f is asymptotically linear at zero and is asymptotically
3linear at infinity. To do this, we also establish a complete
characterization of the spectrum of a nonlocal eigenvalue problem.
Submitted July 4, 2017. Published November 5, 2018.
Math Subject Classifications: 34C23, 47J10, 34C10.
Key Words: Bifurcation; spectrum; nonlocal problem; nodal solution.
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Xiaofei Cao
Faculty of Mathematics and Physics
Huaiyin Institute of Technology
Huaian 223003, China
email: caoxiaofei258@126.com


Guowei Dai
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: daiguowei@dlut.edu.cn

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