Ferreiro Darriba, Juan BoscoCabada Fernández, Alberto2025-02-022025-02-022011-08-01Alberto Cabada, Juan Bosco Ferreiro, First order differential equations with piecewise constant arguments and nonlinear boundary value conditions, Journal of Mathematical Analysis and Applications, Volume 380, Issue 1, 2011, Pages 124-136, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2011.02.054.0022-247Xhttps://hdl.handle.net/10347/39452This paper is devoted to the study of differential equations with piecewise constant arguments coupled with nonlinear boundary value conditions. Under suitable assumptions on the data of the equation, by means of the method of (weakly coupled) lower and upper solutions, we derive the existence of extremal solutions and extremal quasi-solutions. Moreover some results are given concerning the uniqueness of solutions. Furthermore, we deduce some maximum principles related to the linear equation which allow us to develop the monotone iterative method. Some illustrative examples are also presented.engNonlinear boundary value conditionsComparison resultsPiecewise constant argumentsLower and upper solutionsjournal article10.1016/j.jmaa.2011.02.0541096-0813open access