Sentence examples for shall state the existence from inspiring English sources

In this section, we shall state the existence and uniqueness result for solution of BSDE (1.1).

We shall state the global existence of smooth solutions to the linearized problem (19) as follows.

In Section 2 we shall state the definitions and results needed, and in Section 3 we shall establish the existence and uniqueness of the solution to (1.11).

Now we shall state the main result of this paper.

We shall state the definition of differentiability on time scales.

Now, we shall state and prove the following main result.

To apply the variational method with the iterative technique to the existence of solutions for BVP (1.2), we shall state some basic notations and results, which will be used in the proof of our main result.

To apply the variant fountain theorems to the existence of infinitely many solutions for BVP (1.1), we shall state some basic notations and results, which will be used in the proofs of our main results.

To apply critical point theory of the existence of solutions for boundary value problem (1.1), we shall state some basic notation and results, which will be used in the proof of our main results.

The original documents state the "very existence of this agreement" were classified as "secret and shall not to be disclosed by either party".

We shall study the existence of ground state homoclinic orbits for the following non-periodic damped vibration system: u ¨ ( t ) + M u ˙ ( t ) − L ( t ) u ( t ) + H u ( t, u ( t ) ) = 0, t ∈ R, (1.1).