A classical approach to eigenvalue problems associated with apair of mixed regular Sturm-Liouville equations II

[摘要] In the studies of acoustic waveguides in ocean, buckling of columns with variablecross sections in applied elasticity, transverse vibrations in nonhomogeneousstrings, etc., we encounter a new class of problems of the typeL1y1≡−y1′​′+q1(x)y1=λy1defined on an interval[d1,d2]andL2y2≡−y2′​′+q2(x)y2=λy2defined on the interval[d2,d3]satisfying certainmatching conditions at the interface pointx=d2.Earlier, in Part I, we constructed a fundamental system for(L1,L2)and derived certain estimates for the same.Here, in Part II, we consider four types of boundary value problems associated with(L1,L2)and study the corresponding spectra.

[学科分类] 应用数学