School of Mathematics and Physics
North China Electric Power University
Beijing 102206, China
email: weiqifan0924@163.com
School of Mathematics and Physics
North China Electric Power University
Beijing 102206, China
email: zxm74@sina.com
Qifan Wei, Xuemei Zhang
Abstract:
The authors consider the triharmonic equation
$$
(-\Delta)^3u+c_1\Delta^2 u+c_2\Delta u=h(x)|u|^{p-2} u+g(x,u)
$$
in \(\Omega\), where \(p\in(1,2)\), subject to Navier boundary conditions.
Based on the least action principle, the Ekeland's variational principle and a
variant version of mountain pass lemma, we analyze the existence and multiplicity
of nontrivial solutions to the above problem. In addition, we obtain the first
eigenvalue of triharmonic operator and consider its structure.
The conclusions are illustrated with several examples.
Submitted June 23, 2025. Published August 18, 2025.
Math Subject Classifications: 35J30, 35J40.
Key Words: Triharmonic equation; Ekeland's variational principle; mountain pass lemma;
existence and multiplicity of solutions
DOI: 10.58997/ejde.2025.86
Show me the PDF file (417 KB), TEX file for this article.
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Qifan Wei School of Mathematics and Physics North China Electric Power University Beijing 102206, China email: weiqifan0924@163.com |
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Xuemei Zhang School of Mathematics and Physics North China Electric Power University Beijing 102206, China email: zxm74@sina.com |
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