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Displaying similar documents to “Smoothness for the collision local time of two multidimensional bifractional Brownian motions”

Resolvents, integral equations, limit sets

Theodore Allen Burton, D. P. Dwiggins (2010)

Mathematica Bohemica

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In this paper we study a linear integral equation x ( t ) = a ( t ) - ∫ 0 t C ( t , s ) x ( s ) d s , its resolvent equation R ( t , s ) = C ( t , s ) - ∫ s t C ( t , u ) R ( u , s ) d u , the variation of parameters formula x ( t ) = a ( t ) - ∫ 0 t R ( t , s ) a ( s ) 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.