Cabada Fernández, AlbertoInfante, GennaroFernández Tojo, Fernando Adrián2026-02-022026-02-022016-03-01CABADA, Alberto, INFANTE, Gennaro and TOJO, Fernando Adrian. Nonzero solutions of perturbed Hammerstein integral equations with deviated arguments and applications. Topological Methods in Nonlinear Analysis. Online. 1 March 2016. Vol. 47, no. 1, pp. 265 - 287. [Accessed 2 February 2026]. DOI 10.12775/TMNA.2016.005https://hdl.handle.net/10347/45629The final publication is available at the TMNA webpage via https://doi.org/10.12775/TMNA.2016.005We provide a theory to establish the existence of nonzero solutions of perturbed Hammerstein integral equations with deviated arguments, being our main ingredient the theory of fixed point index. Our approach is fairly general and covers a variety of cases. We apply our results to a periodic boundary value problem with reflections and to a thermostat problem. In the case of reflections we also discuss the optimality of some constants that occur in our theory. Some examples are presented to illustrate the theoryengNontrivial solutionsNonlocal boundary conditionsReflectionsDeviated argumentFixed point indexCone1202 Análisis y análisis funcionaljournal article10.12775/TMNA.2016.0051230-3429open access