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

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.