Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of integral equations of the form $u(t)=\int_{G}k(t,s)f(s,u(s))\,ds$, where $G$ is a compact set in $\R^{n}$ and $k$ changes sign, so positive solutions may not exist, $f$ satisfies Carath\'{e}odory conditions and $k$ may be discontinuous. We apply our results to prove the existence of nontrivial solutions of some nonlocal boundary value problems.
Nonzero solutions of Hammerstein integral equations with discontinuous kernels / Infante, Gennaro; Webb, J. R. L.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 272(2002), pp. 30-42.
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Titolo: | Nonzero solutions of Hammerstein integral equations with discontinuous kernels |
Autori: | |
Data di pubblicazione: | 2002 |
Rivista: | |
Citazione: | Nonzero solutions of Hammerstein integral equations with discontinuous kernels / Infante, Gennaro; Webb, J. R. L.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 272(2002), pp. 30-42. |
Handle: | http://hdl.handle.net/20.500.11770/138406 |
Appare nelle tipologie: | 1.1 Articolo in rivista |