Sentence examples for example of equation from inspiring English sources

Theorem 3 has been applied to many equations, see [3, 5] and references therein, but so far no example of equation (1) with a function f increasing in both variables which has stable equilibrium points and stable period-two solutions has been exhibited.

Another nontrivial example of Equation (4) that arises in cycle kinetics in unimolecular systems is due to T.L. Hill [2] [5].

And 2) In the next example, of Equation (18), apparently there is no analytical expression for the eigenvalues, and the final solution for the width of the eigenvactor, Equation (21) still depends on j 0 and w.

2) In the next example, of Equation (18), apparently there is no analytical expression for the eigenvalues, and the final solution for the width of the eigenvactor, Equation (21) still depends on j0 and w.

Moreover, in the first example considered, of Equation (13), the authors simply say that they 'match the eigenvalues to j0 and w, to find that w=pi'.

Now, we present examples of equations for which our method can be applied.

In Section 3, we give some examples of equations modeled by this kind of problems and present some additional remarks.

In Sections 3-5, we have presented several examples of equations from applied mathematics and mathematical physics in which our oscillation-detection program can be carried out successfully.

We also give various examples of equations and boundary conditions satisfying our conditions and also show that our theory can be extended to embrace (C^{1,1}) solutions of degenerate equations.

In the opposite situation, that is, in the superlinear case (alphaexamples of equations of type (3) having solutions of type (6), which can be easily produced, until now no general sufficient conditions for their existence are known.

Show an example of the equation in use.