A generalization of N. Aronszajn's theorem on connectedness of the fixed point set of a compact mapping
On the structure of fixed point sets of some compact maps in the Fréchet space
The aim of this note is 1. to show that some results (concerning the structure of the solution set of equations (18) and (21)) obtained by Czarnowski and Pruszko in [6] can be proved in a rather different way making use of a simle generalization of a theorem proved by Vidossich in [8]; and 2. to use a slight modification of the “main theorem” of Aronszajn from [1] applying methods analogous to the above mentioned idea of Vidossich to prove the fact that the solution set of the equation (24), (25)...
On the structure of the solution set of a functional-differential system on an unbounded interval
It is proved that under some conditions the set of all solutions of an initial value problem for -th order functional differential system on an unbounded interval is a compact .
On the connectedness of the set of fixed points of a compact operator in the Fréchet space
Professor Šeda, septuagenerian
On the number of periodic solutions of a generalized pendulum equation
For a generalized pendulum equation we estimate the number of periodic solutions from below using lower and upper solutions and from above using a complex equation and Jensen’s inequality.
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