Sentence examples for an arbitrary solution of from inspiring English sources

Let be an arbitrary solution of (2.2).

Proof Suppose ( x, y ) is an arbitrary solution of (1).

Let x be an arbitrary solution of this problem.

Let be an arbitrary solution of system (1.5).

Let u be an arbitrary solution of problem (2.1 - 2.3 2.1 - 2.3

Let be an arbitrary solution of (3.1) with period.

Let be any arbitrary solution of (3.34).

Let us consider an arbitrary solution φ of (2.21) on (mathbb{R}_{T}) and the corresponding function (psi: mathbb{R}_{T} tomathbb{R}) given by (2.23).

On the other hand, for an arbitrary solution y n of (2.1), by the unique solvability of the initial value problem (2.1) and (2.3), we have V ( n, P n − 1 y n ) = sup l ∈ Z + ∥ x n + l ( n ; P n − 1 y ) ∥ = sup l ≥ 0 ∥ y n + l ∥.

The approach developed is used to characterize the decay of solutions (by inequalities for the norm of an arbitrary solution and its derivative) in the case of stability, as well as in a general case.

Since B ∗ α [ u ] ( 0 ) = 0, the function v ( x ) must satisfy in addition to the condition v ( 0 ) = 0. Arbitrary solution of the problem (2.4) at smooth f ( x ) and g ( x ) is represented in the form of (4.1).