Symmetric periodic solutions in the Sitnikov problem (Q330086)

The author presents results for the Sitnikov problem -- a simplified problem in celestial mechanics. In the paper, the author presents a number of theorems, lemmas, and propositions and thereby extends results of previous investigations. He shows that there exist odd periodic solutions with a number of zeros for the title problem. Although very specialized, the paper is carefully written and should be of interest to theoreticians working in celestial mechanics and in nonlinear ordinary differential equations.