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Vector integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1999)

Commentationes Mathematicae Universitatis Carolinae

We deal with the integral equation u ( t ) = f ( I g ( t , z ) u ( z ) d z ) , with t I = [ 0 , 1 ] , f : 𝐑 n 𝐑 n and g : I × I [ 0 , + [ . We prove an existence theorem for solutions u L ( I , 𝐑 n ) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1 .

Weak and strong topologies and integral equations in Banach spaces

Donal O'Regan (1995)

Annales Polonici Mathematici

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.

Currently displaying 301 – 320 of 332