Método topologico de t. Wazewski e algumas aplicações ao estudo do comportamento assintotico de sistemas lineares de equações diferenciais ordinarias com perturbações não necessariamente lineares - Nascimento, Arnaldo Simal do (1977)
The objective of this work is to study the asymptotic behavior of ordinary differential equations under not necessarily linear perturbations, using the topological method of WAZEWSKI, wich is shown in the Chapter O. In Chapter 1, considering the linear system (1): x = A(t)x and the perturbed system (2): y = A(t)g + g(t,y), we give conditions such that for every solution x(t), [x(t)] of (1), [2], there is a solution y(t), [x(t)], of (2), [(1)] such that limt→∞ (x(t)-y(t))=0. In the Chapter 2, we give hypothesis under wich we find solutions for the following problems: (i) If x(t) is a solution of (2) and Y/(t) is a fundamental matrix of (1), does there exist a constant n x l matrix b such that x(t) =Y/(t)[(b+0(1)] as t→∞ (ii) If b is a constant n x l ml matrix, does there exist a solution x(t) of (2) such that the above relation holds? In Chapter 3, we give a generalization of a result of Chapter 2 and an application. The mentioned generalization is a corrected version of a result by N.Onuchic and A.Badelucci, wich is shown im [6|