A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm-Liouville equations. II (Q1850706)

The authors consider the pair of Sturm-Liouville equations \[ L_1 y_1\equiv -y_1''+q_1 (x)y_1=\lambda y_1,\;0\leq x\leq h,\;L_2y_2\equiv -y_2''+q_2 (x)y_2= \lambda y_2,\;h\leq x\leq 1, \] together with the matching conditions at the interface \(x=h\) given by \(y_1(h)=y_2(h)\), \(w_1y_1'(h)=w_2y_2'(h)\), where \(\lambda\) is a complex constant, \(q_1\in L_C^2[0,h]\) and \(q_2\in L_C^2[h,1]\). All kinds of boundary conditions at 0 and 1 are considered, i.e., Dirichlet's, Neumann's and the mixed boundary conditions of both types. Under the assumption that \(w_1,w_2\) are reals and that \(|1-{w_1\over w_2} |<{1\over 4}\), the authors obtain several statements concerning the location of eigenvalues and the corresponding eigenfunctions. A physical application is also given. For part I see [ibid. 14, 205-214 (2001; Zbl 0992.34020)].