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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