The paper deals with the existence of solutions for singular higher order differential equations with Sturm–Liouville or (p, n − p) right focal boundary conditions or the (n− p, p) left focal boundary conditions. Righthand sides of differential equations may be singular in the zero values of all their phase variables. The proofs are based on the regularization and sequential techniques. 2000 Ma...

In this paper we consider eigenvalue problems on time scales involving linear Hamiltonian dynamic systems. We give conditions that ensure that the eigenvalues of the problem are isolated and bounded below. The presented results are applicable also to Sturm–Liouville dynamic equations of higher order, and further special cases of our systems are linear Hamiltonian differential systems as well as...