Sentence examples for define the solution from inspiring English sources

In order to define the solution for the problem (1.1 - 1.2 1.1 - 1.2 the followeneedemma.

Next we present an auxiliary lemma to define the solution for problem (1.1 - 1.2 1.1 - 1.2

Step 2. We define the solution of (3.1) by the Perron method.

To define the solution for problem (1.1 - 1.2), we establish the following lemma.

We first define the solution for Eq. (2.1) with initial-boundary condition (2.2) as follows.

A standard approach in deriving the mild solution of (1.1) is define the solution operator Q.

We need to establish the following result to define the solutions for the given problem.

The following lemma plays a pivotal role to define the solutions for the given problem.

Before presenting the main results, we define the solutions of the boundary value problem (1.1).

By introducing dwell time for the topology-varying system, we define the solutions for the closed-loop system equations.

To define the solutions of the problem (1.1), we need the following lemma.