Displaying similar documents to “On a nonlinear integral equation with contractive perturbation.”

Existence of solutions of perturbed O.D.E.'s in Banach spaces

Giovanni Emmanuele (1991)

Commentationes Mathematicae Universitatis Carolinae

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We consider a perturbed Cauchy problem like the following (PCP) x ' = A ( t , x ) + B ( t , x ) x ( 0 ) = x 0 and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).

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.

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.