A remark on the first <em>p</em>-buckling eigenvalue with an adhesive constraint

Yoshihisa Kaga; Shinya Okabe; Yoshihisa Kaga; Shinya Okabe

doi:10.3934/mine.2021035

Mathematics in Engineering

2021, Volume 3, Issue 4: 1-15. doi: 10.3934/mine.2021035

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A remark on the first p-buckling eigenvalue with an adhesive constraint

Yoshihisa Kaga ,
Shinya Okabe ^,

Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

Received: 03 July 2020 Accepted: 23 August 2020 Published: 01 September 2020

We consider a fourth order nonlinear eigenvalue problem with an adhesive constraint. The problem is regarded as a generalization of the buckling eigenvalue problem with the clamped boundary condition. We prove the existence of the first eigenvalue of the problem and show that the corresponding eigenfunction does not have "flat core of adhesion type".
- nonlinear fourth order eigenvalue problem,
- gradient nonlinearity
Citation: Yoshihisa Kaga, Shinya Okabe. A remark on the first p-buckling eigenvalue with an adhesive constraint[J]. Mathematics in Engineering, 2021, 3(4): 1-15. doi: 10.3934/mine.2021035

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Abstract

We consider a fourth order nonlinear eigenvalue problem with an adhesive constraint. The problem is regarded as a generalization of the buckling eigenvalue problem with the clamped boundary condition. We prove the existence of the first eigenvalue of the problem and show that the corresponding eigenfunction does not have "flat core of adhesion type".

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