Abstract and Applied Analysis
Volume 2004 (2004), Issue 7, Pages 577-590
doi:10.1155/S1085337504306299

Nonmonotone impulse effects in second-order periodic boundary value problems

Irena Rachůnková1 and Milan Tvrdý2

1Department of Mathematics, Palack University, Tomkova 40, Olomouc 77200, Czech Republic
2Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, Praha 1 11567, Czech Republic

Received 23 September 2002

Copyright © 2004 Irena Rachůnková and Milan Tvrdý. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We deal with the nonlinear impulsive periodic boundary value problem u″=f(t,u,u′), u(ti+)=Ji(u(ti)), u′(ti+)=Mi(u′(ti)), i=1,2,…,m, u(0)=u(T), u′(0)=u′(T). We establish the existence results which rely on the presence of a well-ordered pair (σ1,σ2) of lower/upper functions (σ1≤σ2 on [0,T]) associated with the problem. In contrast to previous papers investigating such problems, the monotonicity of the impulse functions Ji, Mi is not required here.