Sentence examples for by a solution of from inspiring English sources

For denote by a solution of problem (1.1), (1.6) with.

By a solution of (HIE-1), we understand a mild solution that has a form (3.63).

By a solution of (1.1) we mean a function (xin PC^{2}(mathbb{R})) satisfying (1.1).

By a solution of (1.1) we mean a function in satisfying the relations in (1.1).

Let us define what we mean by a solution of problem (1).

By a solution of (1.1), we mean a real sequence, satisfying (1.1).

Let us start by defining what we mean by a solution of problem (1).

In what follows by a solution of (1.1), (1.11) we mean a solution on.

By a solution of (2.1), we mean a solution of the operator equation (2.5).

end{aligned} By a solution of (1.2 - 1.3 1.2 - 1.3 a solution of system (2.1).

By a solution of (1.1), we mean a nontrivial real-valued function (x t)) satisfying (1.1) for (t inmathbf{T}).