HOMOLOGY PROPERTIES OF THE SETS OF SOLUTIONS TO ORDINARY DIFFERENTIAL-EQUATIONS

The recent studies concerned with existence theorems for solutions to the Dirichlet problem for a second-order ordinary differential equatio n maintain the tradition of using either the Leray-Schauder theory or the properties of the shift operator along trajectories. The same hold s for a large part of the research devoted to existence theorems for p eriodic solutions. However, the first method involves heavy constraint s on the right-hand side of the equation under consideration, while th e results delivered by the second have been weaker so far. In the pres ent paper, results on the persistence of the solutions to the problem in question under a homotopy of the right-hand side (usually derived f rom the Leray-Schauder theory) are proved using ideas relating to the second method and the topological structures suggested earlier by the author, which are adequate for the construction of the sets of solutio ns to ordinary differential equations. The method put forward is insen sitive to complexities in the structure of the right-hand side. Biblio graphy: 9 titles.