Electron. J. Diff. Eqns., Vol. 2006(2006), No. 01, pp. 1-11.

Continuous selections of solution sets to Volterra integral inclusions in Banach spaces

Sergiu Aizicovici, Vasile Staicu

We consider a nonlinear Volterra integral equation governed by an m-accretive operator and a multivalued perturbation in a separable Banach. The existence of a continuous selection for the corresponding solution map is proved. The case when the m-accretive operator in the integral inclusion depends on time is also discussed.

Submitted July 26, 2005. Published January 6, 2006.
Math Subject Classifications: 34G25, 45D05, 45N05, 47H06.
Key Words: Volterra integral equation; m-accretive operator; integral solution; multivalued map.

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Sergiu Aizicovici
Department of Mathematics, Ohio University
Athens, OH 45701, USA
email: aizicovi@math.ohiou.edu
Vasile Staicu
Department of Mathematics, Aveiro University
3810-193 Aveiro, Portugal
email: vasile@ua.pt

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