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On the Aronszajn property for integral equations in Banach space

Stanisław Szufla — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

For the integral equation (1) below we prove the existence on an interval J = [ 0 , a ] of a solution x with values in a Banach space E , belonging to the class L p ( J , E ) , p > 1 . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.

On the Aronszajn property for integral equations in Banach space

Stanisław Szufla — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

For the integral equation (1) below we prove the existence on an interval J = [ 0 , a ] of a solution x with values in a Banach space E , belonging to the class L p ( J , E ) , p > 1 . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.

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