, Volume 13, Issue 1, pp 287–298 | Cite as

The essential spectral radius of Volterra operators and an application to Volterra-Hammerstein functional inclusions

  • Martin Väth


It is shown that for abstract linear Volterra operators the spectral radius is the essential spectral radius. The result is applied to prove the existence of a global solution of a Volterra-Hammerstein functional inclusion when the nonlinearity has at most affine growth.

Mathematics Subject Classification (2000)

45D05 45G10 45N05 47A10 47B65 47H04 47H09 


Abstract Volterra operator essential spectrum measure of noncompactness Leray-Schauder alternative Volterra-Hammerstein functional inclusion nonlinear integral equation multivalued maps 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WürzburgWürzburgGermany

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