Construction of non-constant lower and upper functions for impulsive periodic problems

I. Rachunkova, Department of Mathematics, Palacky University, Olomouc, Czech Republic
M. Tvrdy, Mathematical Institute, Academy of Sciences of the Czech Republic, Prague, Czech Republic

E. J. Qualitative Theory of Diff. Equ., Proc. 7'th Coll. Qualitative Theory of Diff. Equ., No. 19. (2004), pp. 1-8.

Abstract: We present conditions ensuring the existence of piecewise linear lower and upper functions for the nonlinear impulsive periodic boundary value problem
$u''=f(t,u,u'),$ $u(t_i+)=\opJ_i(u(t_i)),$ $u'(t_i+)=\opM_i(u'(t_i)),$ $i=1,2,\dots,m,$ $u(0)=u(T),\,\,u'(0)=u'(T).$
This together with the existence principles which we proved in \cite{rt2}--\cite{rt4} allows us to prove new existence criteria, see Theorems \ref{T3.1} and \ref{T3.2}.

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