Electron. J. Diff. Eqns., Vol. 2007(2007), No. 105, pp. 1-14.

Existence and uniqueness of solutions to first-order systems of nonlinear impulsive boundary-value problems with sub-, super-linear or linear growth

Juan J. Nieto, Christopher C. Tisdell

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.

Submitted March 14, 2007. Published July 30, 2007.
Math Subject Classifications: 34A37, 34B15.
Key Words: Existence and uniqueness of solutions; boundary value problems; impulsive equations; fixed-point theory; system of equations.

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Juan J. Nieto
Departamento de Análisis Matemático
Facultad de Matemáticas
Universidad de Santiago de Compostela
Santiago de Compostela 15782, Spain
email: amnieto@usc.es
Christopher C. Tisdell
School of Mathematics
The University of New South Wales
UNSW Sydney 2052, Australia
email: cct@unsw.edu.au

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