Irena Rachunkova, Department of Math.,
Palacky University, 779 00 OLOMOUC, Tomkova 40, Czech Republic,
Milan Tvrdy, Mathematical Institute, Acad. Sci.of the Czech Republic, 115 67 PRAHA 1, Zitna 25, Czech Republic, e-mail: email@example.com, http://www.math.cas.cz/~tvrdy/;
In this paper, using the lower/upper functions argument, we establish new existence results for the nonlinear impulsive periodic boundary value problem
where f fulfils the Caratheodory conditions on $[0,T]\times R^2$ and $J_i, M_i$ are continuous on R. The main goal of the paper is that the lower/upper functions $\sigma_1 / \sigma_2$ associated with the problem are not well-ordered, i.e. $\sigma_1\not\le\sigma_2$ on [0,T].
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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