Ordinary differential equations on closed subsets of locally convex spaces with applications to fixed point theorems (Q2640763)

The author constructs an approximate solution of the Cauchy problem \(x'=f(t,x)\), \(x(0)=x_ 0\) defined on closed subsets of locally convex topological spaces (real or complex) and shows that under some assumptions (e.g. dissipativity condition or compactness-type condition) the approximate solution converges to a solution. New fixed point theorems for dissipative and \(\alpha\)-condensing maps defined on closed subsets of locally convex topological spaces are given.