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

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

This contribution is part of the Special Issue: Geometric Partial Differential Equations in Engineering
Guest Editor: James McCoy
Link: www.aimspress.com/mine/article/5820/special-articles

Special Issues: Geometric Partial Differential Equations in Engineering

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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Keywords nonlinear fourth order eigenvalue problem; gradient nonlinearity

Citation: Yoshihisa Kaga, Shinya Okabe. A remark on the first p-buckling eigenvalue with an adhesive constraint. Mathematics in Engineering, 2021, 3(4): 1-15. doi: 10.3934/mine.2021035

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