School of Mathematical Sciences
Dalian University of Technology
Dalian, 116024, China
email: liuqingbo@mail.dlut.edu.cn
School of Mathematical Sciences
Dalian University of Technology
Dalian, 116024, China
email: zhaolan@mail.dlut.edu.cn
Qingbo Liu, Lan Zhao
Abstract:
We investigate global bifurcation phenomenon for a class of semilinear eigenvalue
problems involving nonlocal terms. Under certain assumptions, we demonstrate the
existence of a global continuum emanating from the first eigenvalue of the unperturbed
problem. As an application of this result, we identify the parameter interval for which
positive solutions exist in the problem with general nonlinearities \(f\), where \(f\)
exhibits asymptotic \((q-1)\)-linear behavior both near zero and at infinity.
To study the global structure of bifurcation branch, we also establish some properties
of the first eigenvalue for a semilinear eigenvalue problem.
Submitted August 11, 2025. Published November 11, 2025.
Math Subject Classifications: 35B20, 35B32, 35P30.
Key Words: Bifurcation method; nonlocal problem; semilinear eigenvalue problem.
DOI: 10.58997/ejde.2025.105
Show me the PDF file (421 KB), TEX file for this article.
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Qingbo Liu School of Mathematical Sciences Dalian University of Technology Dalian, 116024, China email: liuqingbo@mail.dlut.edu.cn |
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Lan Zhao School of Mathematical Sciences Dalian University of Technology Dalian, 116024, China email: zhaolan@mail.dlut.edu.cn |
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