1 results
DIFFERENTIATING SOLUTIONS OF A BOUNDARY VALUE PROBLEM ON A TIME SCALE
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 94 / Issue 1 / August 2016
- Published online by Cambridge University Press:
- 01 April 2016, pp. 101-109
- Print publication:
- August 2016
-
- Article
-
- You have access
- Export citation
-
We show that the solution of the dynamic boundary value problem
$y^{{\rm\Delta}{\rm\Delta}}=f(t,y,y^{{\rm\Delta}})$, 
$y(t_{1})=y_{1}$, 
$y(t_{2})=y_{2}$, on a general time scale, may be delta-differentiated with respect to 
$y_{1},~y_{2},~t_{1}$ and 
$t_{2}$. By utilising an analogue of a theorem of Peano, we show that the delta derivative of the solution solves the boundary value problem consisting of either the variational equation or its dynamic analogue along with interesting boundary conditions.
