turkmath.org

In this talk we derive Lyapunov type inequalities for the linear 2nx2n Hamiltonian systems with impulsive perturbations. Since changing the impulsive perturbations or assuming different conditions on the impulses leads to different inequalities, presence of the impulse effect provides various Lyapunov type inequalities. Besides, the obtained inequalities are new even in the nonimpulsive case and therefore they improve and generalize the previous ones existing in the literature. As applications of Lyapunov type inequalities, we have found a disconjugacy interval and a lower bound for the associated eigenvalue problems for linear 2n-dimensional Hamiltonian systems under impulse effect.