Displaying similar documents to “On a generalization of the Osgood condition.”

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.

On the Volterra integral equation with weakly singular kernel

Stanisław Szufla (2006)

Mathematica Bohemica

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We give sufficient conditions for the existence of at least one integrable solution of equation x ( t ) = f ( t ) + ∫ 0 t K ( t , s ) g ( s , x ( s ) ) d s . Our assumptions and proofs are expressed in terms of measures of noncompactness.