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Accurate asymptotic formulas for eigenvalues and eigenfunctions of a boundary-value problem of fourth order. (English) Zbl 1214.47021

Accurate asymptotic formulas are obtained for the eigenvalues and eigenfunctions of the nonself-adjoint fourth-order periodic boundary value problem \[ \begin{aligned} &u^{(4)}(t)+q(x)y=\lambda y, \quad 0\leq x\leq \pi,\\ &y^{(j)}(0)-y^{(j)}(\pi)=0,\quad j=0, 1, 2, 3, \end{aligned} \]
where \(q(x)\) is a complex valued function satisfying \(\int_0^{\pi}q(x)\, dx=0.\)

MSC:

47A99 General theory of linear operators
47N20 Applications of operator theory to differential and integral equations
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References:

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