On existence of a bounded solution in a problem with a control parameter
- Shchetinina, Ekaterina
2010 Mathematics Subject Classification
- 34A34 34C11
- bounded solutions, delayed loss of stability, gluing
This paper is devoted to the problem of existence of bounded solutions for non-autonomous differential equations in the case when the linear part has a pair of simple complex conjugate eigenvalues crossing the imaginary axis for increasing $t$. By introducing a control parameter into the system we derive conditions for the existence of a global uniformly bounded solution.