Sentence examples for be a damped solution from inspiring English sources

Let be a damped solution.

Let be a damped solution of problem (1.1), (1.10).

Then is a damped solution.

If is a damped solution, then is oscillatory and its amplitudes are decreasing.

We see, by (2.12), that is a damped solution of problem (1.1), (1.10) if and only if is a damped solution of problem (2.13), (1.10).

Then is just one of the following four types: (I) is an escape solution;   (II) is a homoclinic solution;   (III) is a damped solution;   (IV) is a non-monotonous solution.  . is an escape solution; is a homoclinic solution; is a damped solution; is a non-monotonous solution.

Let and be the set of all such that is a damped solution and an escape solution, respectively.

If is a damped solution of problem (1.1), (1.10), then has a finite number of isolated zeros and satisfies (2.21); or is oscillatory (it has an unbounded set of isolated zeros).

Then, by Lemma 2.6, either fulfils (2.21) or has its second zero and, arguing as in Steps 2 5 of the proof of Theorem 3.3, we deduce that is a damped solution.

Then is called a damped solution.

If ( or ), then is called a damped solution (a homoclinic solution or an escape solution) of problem (1.1), (1.7).