On asymptotic behaviour of solutions of certain classes of ordinary differential equations (Q1183242)

The author considers the system of differential equations \(y'=A(x)y+a(x,y,z)\), \(z'=B(x)z+b(x,y,z)\), where \(x\in I:=[x_ 0,\infty)\), \(y\in R^ k\), \(z\in R^ s\), \(k,s\geq 1\). Using the topological method of T. Ważewski he proves the existence of a family of solutions majorized componentwise by appropriate functions on \(I\). He applies this result to the study of asymptotic equivalence of systems, conditional stability of solutions, and the existence of solutions of singular Cauchy problems.