Sentence examples for a solution for the difference from inspiring English sources

In fact, we clearly see that the sequence is such a solution for the difference system.

We can check that (x^) is a solution for the system of fractional difference inclusions (1).

However agreement on using similar criteria and a standard measure to assess premenstrual disorders in adolescents might be a solution for the problem of such differences in reporting.

Now, we are ready to provide our result on the existence of a solution for the k-dimensional system of fractional finite difference inclusions (1).

Theorem 3 Assuming that A has no eigenvalues with modulus one and that f is u.s.p. and Lipschitzian w.r.t. the second variable with a sufficiently small constant, there exists a unique semi-periodic solution for the difference equation (1).

Existence of the solutions for the difference scheme has been shown.

As this trend is expected to persist, the importance of aquaculture, as the solution for providing the difference between the demand and the biomass available, could increase.

So there is only the zero solution for the homogeneous difference equation (17).

By a positive solution for the fractional q-difference system (1.1) we mean a mapping with positive components on [ 0, 1 ] such that (1.1) is satisfied.

(1.6) Ma and Guo [9] proved the existence of a nontrivial homoclinic solution for the second order difference equations Delta (p_{n}Delta u_{n-1} )+q_{n}u_{n}=f (n,u_{n} ),quad ninBbb {Z} (1.7) in terms of the Mountain Pass theorem relying on Ekeland's variational principle and the diagonal method.

Yan and Liu [23] provided the existence of a bounded nonoscillatory solution for the third order difference equation begin{aligned}& Delta^{3}x(n)+f bigl(n,x(n),x n-r) bigr)=0, quad ngeq n_{0} end{aligned} (1.9) and got a necessary and sufficient condition for Eq. (1.9) to have a bounded nonoscillatory solution ({x n-r_{ngeq n_{0}}) with (lim_{nrightarrowinfty}x(n)=d).