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non-zero solution

Proceedings of the Edinburgh Mathematical Society (1)

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EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS
Gennaro Infante
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 46 / Issue 1 / February 2003

Published online by Cambridge University Press:

27 January 2003, pp. 75-86
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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