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Eigenvalues of fourth-order boundary value problems with distributional potentials
AIMS Mathematics 2022, 7(5): 7294-7317
Published: 15 May 2022
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This paper aims to investigate the fourth-order boundary value problems with distributional potentials. We first prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real. Then we obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problems: the boundary conditions, the coefficient functions and the endpoints. Moreover, we find the differential expressions for each parameter.

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