Abstract

We study a one dimensional version of a problem that arises in mathematical modeling for burglary of houses. Our approach uses techniques inspired by coincidence degree, see Mawhin (1979). A priori estimates are obtained through a somewhat unusual combination of estimates based upon maximum or minimum properties and on L-1-estimates of the type introduced by Ward, see Ward (1981) in some periodic problems. (C) 2013 Elsevier Ltd. All rights reserved.