EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS

Abstract

Abstract 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 a possibly discontinuous function that is allowed to change sign. We apply our results to prove existence of eigenvalues of some non-local boundary-value problems. AMS 2000 Mathematics subject classification: Primary 34B10. Secondary 34B18; 47H10; 47H30