On the characteristic functions and Dirchlet-integrable solutions of singular left-definite Hamiltonian systems
The authors consider the following equation\N\[\N-\left( py^{\prime}\right) ^{\prime}+qy=\lambda\omega y,~x\in\left[ a,b\right) ,\N\]\Nwith a singular left-definite Hamiltonian system\N\[\NJY^{\prime}=\left( \lambda A+B\right) Y,\N\]\Nwhere \(J,A,B\) are \(r\times r\) matrices such that \(J\) is a constant matrix satisfying \(J^{\ast}=-J,\) \(A\) and \(B\) are locally integrable matrix-functions on \(\left[ a,b\right) \) satisfying \(A^{\ast}=A\) and \(B^{\ast}=B.\) They study the characteristic-matrix theory of the system and some results on its Dirichlet-integrable solutions.
scientific article; zbMATH DE number 7858260
scientific article