A class of boundary value problems for the Sturm-Liouville operator (Q2703936)

The author considers spectral boundary value problems for the nonselfadjoint Sturm-Liouville operator \(Lu=u''-q(x)u\) defined on the interval \((0,1)\), where \(q(x)\) is a complex-valued function of the class \(W_1^1[0,1]\). NEWLINENEWLINENEWLINEThe presented theorems give conditions for the simplicity of eigenvalues and estimations on solutions to the following boundary value problems: NEWLINE\[NEWLINELu+\mu^2u=0, \quad u(0)=0, \quad u'(1)+\varepsilon u(1) = u'(1/2), \quad \varepsilon\geq 0NEWLINE\]NEWLINE and NEWLINE\[NEWLINELu+\mu^2 u=0, \quad B_1(u)=0, \quad B_2(u)=0,NEWLINE\]NEWLINE where \(B_1\) and \(B_2\) are linearly independent forms \(B_i(u)=a_{1,i}u'(0)+b_{1,i}u'(1)+a_{0,i}u(0)+b_{0,i}u(1)\). Here, \(\varepsilon\geq 0\), \(a_{1,i}\), \(b_{1,i}\), \(a_{0,i}\), \(b_{0,i}\) are some constants.