Abstract
We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II1. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues and eigenfunctions of the problems asm→−0.
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Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999.
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Ben Amara, J., Shkalikov, A.A. A sturm-liouville problem with physical and spectral parameters in boundary conditions. Math Notes 66, 127–134 (1999). https://doi.org/10.1007/BF02674866
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DOI: https://doi.org/10.1007/BF02674866