**9. Asymptotics of Solutions in the Case** *b* **= 0 and** *d >* **0**

Firstly, consider the initial conditions from *S*+. Similar to the case in Section 2, we obtain that for all *t* ≥ 0, the solution has the form of (5).

Therefore, in the case that *b* = 0 and *d* > 0, all solutions with initial conditions from the set *S*<sup>+</sup> tend to a constant *λd* at *t* → +∞.

Now consider the initial conditions from *S*−. If function *f* satisfies Inequality (38), then we obtain that Equation (2) has a negative relaxation cycle (all the reasoning is the same as in Section 8).

The following statement is true.

**Theorem 7.** *Let b* = 0*, d* > 0*, and let condition* (38) *be true. Then, for all sufficiently large λ* > 0*, Equation* (2) *has a negative relaxation cycle with the asymptotics of* (41) *and period t*<sup>∗</sup> = 2*T* + (1 + *o*(1))ln *λ at λ* → +∞*.*

Let us construct the asymptotics of the solution to Equation (2) in the case that function *f* satisfies the inequality (42). Similarly to Section 8, in the segment *t* ∈ [0, *T*], the solution has the form of (36), in the segment *t* ∈ [*T*, 2*T*], it has the form of (37), and in the segment *t* ∈ [2*T*, 3*T*], it has the form of (43). Since Expression (43) is greater than *pR* for all *t* > 2*T*, Equation (2) has the form of (4) for all *t* > 3*T*, and the solution has the form of (43) for all *t* > 2*T*.

Thus, in the case that *b* = 0 and *d* > 0, under the condition that function *f* satisfies Inequality (42), all solutions with initial conditions from the set *S*<sup>−</sup> tend to a constant *λd* at *t* → +∞.
