A Granas type approach to some continuation theorems and periodic boundary value problems with impulses. (English) Zbl 0847.34028

Precup, Radu

Topol. Methods Nonlinear Anal. 5, No. 2, 385-396 (1995).

In 1990 A. Capietto, J. Mawhin and F. Zanolin [J. Differ. Equations 88, 347-395 (1990; Zbl 0718.34053)] proved certain versions of the continuation theorem for the case of the non-existence of a priori bounds of solutions. The author has been inspirated by this paper and he has proved some modification of these results by means of essential maps without the degree theory. As an application of these results he gets the existence of a periodic solution to a second order ordinary differential equation subject to some impulses at certain points.

Reviewer: I.Rachůnková (Olomouc)

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
47H10	Fixed-point theorems

Keywords:

continuation theorem; essential maps; degree theory; periodic solution; second order ordinary differential equation subject to some impulses

Citations:

Zbl 0718.34053