Nontrivial solutions of systems of Hammerstein integral equations with first derivative dependence

摘要

By means of classical fixed point index, we prove new results on theexistence, non-existence, localization and multiplicity of nontrivial solutionsfor systems of Hammerstein integral equations where the nonlinearities areallowed to depend on the first derivative. As a byproduct of our theory wediscuss the existence of positive solutions of a system of third order ODEssubject to nonlocal boundary conditions. Some examples are provided in order toillustrate the applicability of the theoretical results.