Sentence examples for description of the solutions from inspiring English sources

In this paper we used p-regularity theory to prove the existence of solutions of the nonlinear Duffing equation and gave an approximate description of the solutions set.

As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity.

The large time behavior of the solutions of (1.1) is discussed in Section 2 and our general result on the asymptotic description of the solutions (1.5) is presented in Section 3. In this section, we prove the existence of the limit (1.3) for the solutions of (1.1).

It seems that only the discrete formulation gives a consistent description of the solution.

The following is a useful description of the solution profile for the extremals on (mathbb {R}^n_+).

This paper presents a formal description of the solution and an initial sketch of the required proofs of correctness.

In fact, the description of the solution in our framework is "redundant" as an inference chain of automatic model composition.

We explore in detail the properties of the resonant response and provide a unified topological description of the solution.

As an immediate special case of Theorem 3.5, we have the following explicit description of the solution coefficients in terms of the previous coefficient.

An explicit description of the solution of the model problem (in terms of Fourier multipliers) and resulting estimates can be found in Section 3.

Section 4 presents a detailed description of the solution detailing how each component works including a mathematical model of the proposed mechanism.