Displaying similar documents to “Solutions for a class of integro-differential equations with time periodic coefficients.”

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.

Weak and strong topologies and integral equations in Banach spaces

Donal O'Regan (1995)

Annales Polonici Mathematici

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The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of L α and C solutions to Volterra and Hammerstein integral equations in Banach spaces.