A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm-Liouville equations I
نویسندگان
چکیده
منابع مشابه
A Classical Approach to Eigenvalue Problems Associated with a Pair of Mixed Regular Sturm - Liouville Equations
In the studies of acoustic waveguides in ocean, buckling of columns with variable cross sections in applied elasticity, transverse vibrations in non-homogeneous strings, etc., we encounter a new class of problems of the d2 yl X-2-rUl()Yl-"Yl defined on an interval [dl,d2] and type L lyldy L2Y2 + q2(x)y2 .y2 on the adjacent interval [d2, d3] satisfying certain matching conditions at the interfac...
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The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on the problem. An expression for the derivative of the n-th eigenvalue with respect to a given parameter: an endpoint, a boundary condition constant, a coefficient or weight function, is found.
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Given any self-adjoint realization S of a singular Sturm-Liouville (S-L) problem, it is possible to construct a sequence {Sr} of regular S-L problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of {Sr} (ii) in the case when S is regular or limit-circle at each endpoint, a convergent sequence of ei...
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We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and −K are extrema of the eigencurves of this family. This characterization mak...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics and Stochastic Analysis
سال: 2001
ISSN: 1048-9533,1687-2177
DOI: 10.1155/s1048953301000168