Perturbation of time scale quadratic functionals with variable endpoints

• Authors: HILSCHER Roman; RŮŽIČKOVÁ Viera
• Year of publication: 2007
• Type: Article in Periodical
• Magazine / Source: Advances in Dynamical Systems and Applications
• MU Faculty or unit: Faculty of Science
• Field: General mathematics
• Keywords: Linear Hamiltonian system; nonnegativity; positivity; quadratic funcfunctional; time scale; time scale symplectic system
• Description: In this paper we establish perturbation results pertaining the nonnegativity and positivity of a time scale quadratic functional F₀ and its perturbations of the form G(x, u) = F₀(x, u) + alpha || x(a) ||² + beta || x(b) ||², where the endpoints of the functional F₀ are zero while the endpoints of the functional G can vary. These functionals are closely related to time scale symplectic systems. Moreover, we extend such results to functionals with variable endpoints. The results of this paper generalize perturbation results recently known for the special case of the discrete time, but they are new for the continuous time.

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