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Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems
  • Bertin Zinsou
Bertin Zinsou
University of the Witwatersrand

Corresponding Author:[email protected]

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Abstract

Fourth order problems with the differential equation $y^{(4)}-(gy’)’=\lambda^2y$, where $g\in C^1[0,a]$ and $a>0$, occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation $y^{(4)}-(gy’)’=\lambda^2y$ and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.