Theoretical foundations of the study of a certain class of hybrid systems of differential equations (Q2662929)

A hybrid system of differential equations is a system containing both ordinary and partial differential equations. Systems of this form appear when using the Hamilton-Ostrogradsky variational principle for the derivation of equations of motion for mechanical systems. In this paper, the author considers boundary-value problems for a hybrid system of differential equations containing the Dirac delta-function in their coefficients. The presence of the Dirac delta-function in the coefficients of the system leads to the necessity of considering generalized solutions of hybrid systems. The author investigates the eigenvalues and frequency equation of the boundary-value problem for hybrid system and gives some numerical simulations in comparison with previous studies.