Irena Rachunkova and Milan Tvrdy

Periodic Boundary Value Problems for Nonlinear
Second Order Differential Equations with Impulses - Part I

Irena Rachunkova and Milan Tvrdy

In this paper, using the lower/upper functions argument, we establish new existence results for the nonlinear impulsive periodic boundary value problem

u''=f(t,u,u'); u(t_i+)=J_i(u(t_i)), u'(t_i+)=M_i(u'(t_i)), i=1,2,..., m; u(0)=u(T), u'(0)=u'(T).

where f fulfils the Caratheodory conditions on [0,T] x R² and J_i, M_i are continuous on R. The main goal of the paper is that the lower/upper functions σ₁/σ₂ associated with the problem are not well-ordered.

Mathematics Subject Classification 2000. 34B37, 34B15, 34C25

Keywords. Second order nonlinear ordinary differential equation with impulses, periodic solutions, lower and upper functions, Leray-Schauder topological degree, a priori estimates.