Rachůnková, I.; Tvrdý, M. Non-ordered lower and upper functions in second order impulsive periodic problems. (English) Zbl 1086.34026 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 12, No. 3-4, 397-415 (2005). 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. Reviewer: Sotiris K. Ntouyas (Ioannina) Cited in 22 Documents MSC: 34B37 Boundary value problems with impulses for ordinary differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations Keywords:second-order nonlinear ordinary differential equation PDFBibTeX XMLCite \textit{I. Rachůnková} and \textit{M. Tvrdý}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 12, No. 3--4, 397--415 (2005; Zbl 1086.34026)