A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm-Liouville equations I

[摘要] 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 thetypeL1y1=−d2y1dx2+q1(x)y1=λy1defined on an interval[d1,d2]andL2y2=−d2y2dx2+q2(x)y2=λy2on the adjacent interval[d2,d3]satisfying certain matching conditions at the interface pointx=d2.Here in Part I, we constructed a fundamental system for(L1,L2)and derive certain estimates for the same. Later, in Part II, we shall consider four types of boundary value problems associated with(L1,L2)and study the corresponding spectra.

[学科分类] 应用数学