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, {Z}itná 25, Praha 1 11567, Czech Republic

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.