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

Abstract

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

18 pages

References in corpus (1)

• Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains

Cited by in corpus (2)

• Nontrivial solutions of systems of perturbed Hammerstein integral equations with functional terms
• Semi linear elliptic systems with dependence on the gradient