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.
Show me the PDF file (271 KB), TEX file, and other files for this article.
 |
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 |
Return to the EJDE web page