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Non-ordered lower and upper functions in second order impulsive periodic problems. (English) Zbl 1086.34026

The authors prove existence results for the following nonlinear impulsive periodic boundary value problem \[ u''=f(t,u,u') \]
\[ u(t_i+)={\mathcal J}(u(t_i)), \quad u'(t_i+)={\mathcal M}(u'(t_i)), \quad i=1,2,\ldots,m, \]
\[ u(0)=u(T),\quad u'(0)=u'(T), \] where \(f\in \text{Car}([0,T]\times {\mathbb R}^2)\) and \({\mathcal J}_i, {\mathcal M}_i\in C({\mathbb R}), i=1,2,\ldots,m.\) They use the lower/upper functions argument in the case that they are not well-ordered. Some illustrative examples are also provided.

MSC:

34B37 Boundary value problems with impulses for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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