Geodesic
Resolvents, integral equations, limit sets
Mathematica Bohemica, Tome 135 (2010) no. 4, pp. 337-354.

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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.
DOI : 10.21136/MB.2010.140824
Classification : 34D20
Keywords: integral equation; resolvent 
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Burton, T. A.; Dwiggins, D. P. Resolvents, integral equations, limit sets. Mathematica Bohemica, Tome 135 (2010) no. 4, pp. 337-354. doi : 10.21136/MB.2010.140824. http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140824/

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