On topological properties of solution sets of non Lipschitzian quantum stochastic differential inclusions
- 84 Downloads
In this paper, we establish results on continuous mappings of the space of the matrix elements of an arbitrary nonempty set of pseudo solutions of non Lipschitz quantum Stochastic differential inclusion (QSDI) into the space of the matrix elements of its solutions. we show that under the non Lipschitz condition, the space of the matrix elements of solutions is still an absolute retract, contractible, locally and integrally connected in an arbitrary dimension. The results here generalize existing results in the literature.
KeywordsNon classical ODI Non-Lipschitz function Topological properties Matrix elements
Mathematics Subject Classification60H10 60H20 65L05 81S25
- 4.Bishop, S.A.: Existence and Variational Stability of Solutions of Kurzweil Equations associated with Quantum Stochastic Differential Equations. PhD Thesis, Covenant University Ota, Ogun State, Nigeria (2012)Google Scholar
- 8.Kurzweil, J.: Problems which lead to a generalization of the concept of ordinary differential equation. Differential Equations and their Applications. Czech Academy of Science, Prague (1963)Google Scholar