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
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.
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
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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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