Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth
Date
2007-07-30
Authors
Nieto, Juan J.
Tisdell, Christopher
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
In 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.
Description
Keywords
Existence and uniqueness of solutions, Boundary value problems, Impulsive equations, Fixed-point theory, System of equations
Citation
Nieto, 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.
Rights
Attribution 4.0 International