# A Granas type approach to some continuation theorems and periodic boundary value problems with impulse

## Abstract

In this paper we study periodic solutions of a second order differential equation
$x^{\prime\prime} = f(t, x, x^{\prime}) \quad for \ a.e. \ t\in [0, 1],$
subject to some impulses at certain points.

Our work was inspired by a paper by Capietto–Mawhin–Zanolin [1], where the case of no impulses was treated.

The major difference between paper [1] and ours is that instead of topological degree, we use the elementary method based on essential maps. In this context, we also give some new contributions to Granas’ theory of continuation principles.

## Authors

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

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## Paper coordinates

R. Precup, A Granas type approach to some continuation theorems and periodic boundary value problems with impulses, Topological Methods in Nonlinear Analysis, 5 (1995) no. 2, 385-396.

## PDF

##### Journal

Topological Methods in Nonlinear Analysis

12303429

MR: 97a:34028