Sentence examples for proved the solution of from inspiring English sources

Under some conditions, they proved the solution of (1.3) blows up in finite time and even blows up globally.

In this section, we will prove the solution of equation (1.3) can generate a MRDS, and the MRDS posses a random attractor.

These results are useful for proving the solutions of nonlinear functional differential and integral equations which may depend upon the past history, present data and future consideration.

It is proved that the solution of these problems converge to the exact derivatives with order (O(h^{4})).

Now we prove that the solution of problem is unique.

In the following we will prove that the solution of model (2.2) is ultimately bounded.

We first prove that the solution of (2.1) can be expressed as (2.2).

We prove that the solution of an appropriate optimization problem leads to such an interpolant.

It is easy to prove that the solution of the system (1.4) which satisfies the initial condition is positive.

We now prove that the solution of VI(1.1) is unique in X ⋂ K under the condition (I).

By Theorem 3.1 and Remark 5.1, it is easy to prove that the solution of (1.1) and (1.2) is bounded.