Electron. J. Diff. Eqns., Vol. 2008(2008), No. 103, pp. 1-11.

On non-absolute functional Volterra integral equations and impulsive differential equations in ordered Banach spaces

Seppo Heikkila, Seppo Seikkala

In this article we derive existence and comparison results for discontinuous non-absolute functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. The obtained results are then applied to first-order impulsive differential equations.

Submitted April 24, 2008. Published August 6, 2008.
Math Subject Classifications: 26A39, 28B15, 34G20, 34K45, 45N05, 46E40, 47H07.
Key Words: HL integrability; Bochner integrability; ordered Banach space; dominated convergence; monotone convergence; integral equation; boundary value problem

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Seppo Heikkilä
Department of Mathematical Sciences, University of Oulu
Box 3000, FIN-90014 University of Oulu, Finland
email: seppo.heikkila@oulu.fi
Seppo Seikkala
Division of Mathematics, Department of Electrical Engineering
University of Oulu, 90570 Oulu, Finland
email: seppo.seikkala@ee.oulu.fi

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