Preprint no. 153
Mathematical Institute of the Academy of Sciences of the Czech Republic

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

Irena Rachunkova and Milan Tvrdy

Irena Rachunkova, Department of Math., Palacky University, 779 00 OLOMOUC, Tomkova 40, Czech Republic, e-mail: rachunko@risc.upol.cz;
Milan Tvrdy, Mathematical Institute, Acad. Sci.of the Czech Republic, 115 67 PRAHA 1, Zitna 25, Czech Republic, e-mail: tvrdy@math.cas.cz, http://www.math.cas.cz/~tvrdy/;

Summary:

This paper provides existence results for the nonlinear impulsive periodic boundary value problem

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

where  f   satisfies the Carathéodory conditions and    J_i, M_i   are continuous. The basic assumption is the existence of lower/upper functions associated with the problem. Here we generalize and extend the existence results of our previous papers.

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

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

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