His proof is based on the transformation of the time variable which causes problems in the time scale setting.
The obtained results are even new for the special cases of difference equations and differential equations, as well as in the general time scale setting.
This process leads to a decreasing sequence of time scale sets: mathbb{T}supsetmathbb{T}_{1}supsetmathbb{T}_{2} supsetcdotssupset mathbb{T}_{n}supsetcdots.
The results are even new for the special cases of difference equations and differential equations, as well as in the general time scale setting.
Recently, when is -Laplacian operator, that is, and the nonlinear term does not depend on the first-order derivative, the existence problems of positive solutions of boundary value problems have attracted much attention, see [10, 12, 15 22] in the continuous case, see [15, 23 25] in the discrete case and [11, 13, 14, 26, 27] in the general time scale setting.
The pressure forces play a destabilizing role against the stabilizing viscous forces, with oscillatory time scales set by either external flapping or the intrinsic flow body coupling.
With these experiments, we provide the first evidence that RNA circuits can propagate signals at time scales set by their degradation rates and showed that this leads to circuit response times on the order of 15 20 min. This is nearly 6 times faster than circuits constructed from stable proteins, which have response times set by the cell doubling time.
These results are even new for the corresponding differential and difference equation as well as in general time scales setting.
The authors claimed that "we note that this is the first work (to our knowledge) that deals with singular boundary value problems in a general time scales setting".
To our best knowledge, this result is new in the time scales setting and it covers the results not only for ordinary differential equations but also difference equations, q-difference equations, and other exotic time scales.
