Nieto, Juan J.Tisdell, Christopher2021-08-132021-08-132007-07-30Nieto, J. J., & Tisdell, C. C. (2007). Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth. <i>Electronic Journal of Differential Equations, 2007</i>(105), pp. 1-14.1072-6691https://hdl.handle.net/10877/14321In this work we present some new results concerning the existence and uniqueness of solutions to an impulsive first-order, nonlinear ordinary differential equation with "non-periodic" boundary conditions. These boundary conditions include, as a special case, so-called "anti-periodic" boundary conditions. Our methods to prove the existence and uniqueness of solutions involve new differential inequalities, the classical fixed-point theorem of Schaefer, and the Nonlinear Alternative. Our new results apply to systems of impulsive differential equations where the right-hand side of the equation may grow linearly, or sub- or super-linearly in its second argument.Text14 pages1 file (.pdf)enAttribution 4.0 InternationalExistence and uniqueness of solutionsBoundary value problemsImpulsive equationsFixed-point theorySystem of equationsArticle