Spectral Analysis of Higher-Order Differential Operators II: Fourth-Order Equations |
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Authors: | Remling Christian |
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Institution: | FB Mathematik/Informatik, Universität Osnabrück 49069 Osnabrück, Germany. E-mail: christian.remling{at}mathematik.uni-osnabrueck.de |
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Abstract: | We investigate the location and nature of the spectrum of thefourth-order self-adjoint equation (p0 y')'+(p1 y')'+qy=zwy subject to certain asymptotic assumptions on the coefficients.The main tools are the theory of asymptotic integration andthe TitchmarshWeyl M-matrix. Asymptotic integration yieldsasymptotic formulae for the solutions of the differential equationwhich are then used to derive properties of the M-matrix. Thecharacterisation of spectral properties in terms of the boundarybehaviour of M leads to the desired results. |
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