Resolvents, integral equations, limit sets
Theodore Allen Burton; D. P. Dwiggins
Mathematica Bohemica (2010)
- Volume: 135, Issue: 4, page 337-354
- ISSN: 0862-7959
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topBurton, Theodore Allen, and Dwiggins, D. P.. "Resolvents, integral equations, limit sets." Mathematica Bohemica 135.4 (2010): 337-354. <http://eudml.org/doc/197147>.
@article{Burton2010,
abstract = {In this paper we study a linear integral equation $x(t)=a(t)-\int ^t_0 C(t,s) x(s) \{\rm d\} s$, its resolvent equation $R(t,s)=C(t,s)-\int ^t_s C(t,u)R(u,s) \{\rm d\} u$, the variation of parameters formula $x(t)=a(t)-\int ^t_0 R(t,s)a(s) \{\rm d\} s$, and a perturbed equation. The kernel, $C(t,s)$, satisfies classical smoothness and sign conditions assumed in many real-world problems. We study the effects of perturbations of $C$ and also the limit sets of the resolvent. These results lead us to the study of nonlinear perturbations.},
author = {Burton, Theodore Allen, Dwiggins, D. P.},
journal = {Mathematica Bohemica},
keywords = {integral equation; resolvent; linear integral equation; resolvent equation; nonlinear perturbations},
language = {eng},
number = {4},
pages = {337-354},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Resolvents, integral equations, limit sets},
url = {http://eudml.org/doc/197147},
volume = {135},
year = {2010},
}
TY - JOUR
AU - Burton, Theodore Allen
AU - Dwiggins, D. P.
TI - Resolvents, integral equations, limit sets
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 4
SP - 337
EP - 354
AB - In this paper we study a linear integral equation $x(t)=a(t)-\int ^t_0 C(t,s) x(s) {\rm d} s$, its resolvent equation $R(t,s)=C(t,s)-\int ^t_s C(t,u)R(u,s) {\rm d} u$, the variation of parameters formula $x(t)=a(t)-\int ^t_0 R(t,s)a(s) {\rm d} s$, and a perturbed equation. The kernel, $C(t,s)$, satisfies classical smoothness and sign conditions assumed in many real-world problems. We study the effects of perturbations of $C$ and also the limit sets of the resolvent. These results lead us to the study of nonlinear perturbations.
LA - eng
KW - integral equation; resolvent; linear integral equation; resolvent equation; nonlinear perturbations
UR - http://eudml.org/doc/197147
ER -
References
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