Xiaofei Cao, Guowei Dai
In this article, we consider a Dancer-type unilateral global bifurcation for the Kirchhoff-type 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 Kirchhoff-type problem
where f 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.
Submitted July 4, 2017. Published November 5, 2018.
Math Subject Classifications: 34C23, 47J10, 34C10.
Key Words: Bifurcation; spectrum; nonlocal problem; nodal solution.
Show me the PDF file (243 KB), TEX file for this article.
| Xiaofei Cao |
Faculty of Mathematics and Physics
Huaiyin Institute of Technology
Huaian 223003, China
| Guowei Dai |
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
Return to the EJDE web page