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EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS

Published online by Cambridge University Press:  27 January 2003

Gennaro Infante
Gennaro Infante
Affiliation:
Dipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy ([email protected])
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Abstract

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Working on a suitable cone of continuous functions, we give new results for integral equations of the form$\lambda u(t)=\int_{G}k(t,s)f(s,u(s))\,\mathrm{d} s:=Tu(t)$, where $G$ is a compact set in $\mathbb{R}^{n}$ and $k$ is apossibly discontinuous function that is allowed to change sign. We apply our results to prove existence of eigenvaluesof some non-local boundary-value problems.

AMS 2000 Mathematics subject classification: Primary 34B10. Secondary 34B18; 47H10; 47H30

Keywords

fixed-point indexconenon-zero solution
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 1 , February 2003 , pp. 75 - 86
Copyright
Copyright © Edinburgh Mathematical Society 2003