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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 thetype L1y1=−d2y1dx2+q1(x)y1=λy1 defined on an interval [d1,d2] andL2y2=−d2y2dx2+q2(x)y2=λy2 on the adjacent interval [d2,d3] satisfying certain matching conditions at the interface point x=d2

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