Electron. J. Diff. Eqns., Vol. 2009(2009), No. 58, pp. 1-30.

Nonnegative solutions to an integral equation and its applications to systems of boundary value problems

Ioannis K. Purnaras

Abstract:
We study the existence of positive eigenvalues yielding nonnegative solutions to an integral equation. Also we study the positivity of solutions on specific sets. These results are obtained by using a fixed point theorem in cones and are illustrated by application to systems of boundary value problems.

Submitted February 27, 2009. Published April 24, 2009.
Math Subject Classifications: 34B18, 34A34.
Key Words: Nonnegative solutions;integral equation; eigenvalue; systems of boundary value problems.

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Ioannis K. Purnaras
Department of Mathematics
University of Ioannina
P. O. Box 1186, 451 10 Ioannina, Greece
email: ipurnara@cc.uoi.gr

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