Oscillation of symplectic dynamic systems

Oscillation of Symplectic Dynamic Systems

We investigate oscillatory properties of a perturbed symplectic dynamic system on a time scale that is unbounded above. The unperturbed system is supposed to be nonoscillatory, and we give conditions on the perturbation matrix, which guarantee that the perturbed system becomes oscillatory. Examples illustrating the general results are given as well.

Oscillation Theorems for Symplectic Difference Systems

We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same pr...

Symplectic Difference Systems: Oscillation Theory and Hyperbolic Prüfer Transformation

dynamic coloring of graph

در این پایان نامه رنگ آمیزی دینامیکی یک گراف را بیان و مطالعه می کنیم. یک –kرنگ آمیزی سره ی رأسی گراف g را رنگ آمیزی دینامیکی می نامند اگر در همسایه های هر رأس v?v(g) با درجه ی حداقل 2، حداقل 2 رنگ متفاوت ظاهر شوند. کوچکترین عدد صحیح k، به طوری که g دارای –kرنگ آمیزی دینامیکی باشد را عدد رنگی دینامیکی g می نامند و آنرا با نماد ?_2 (g) نمایش می دهند. مونت گمری حدس زده است که تمام گراف های منتظم ...

Oscillation of Two-Dimensional Neutral Delay Dynamic Systems

−q(t)f 2 (x(τ 2 (t))). We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results when a(t) = 0 improve the oscillation results for dynamic systems on time scales that have been established by Fu and Lin (2010), since our results do not restrict to the case where f(u) = u. Also, as a special case when T = R, our results do not require a n to be a ...