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 to illustrate the applicability of the theoretical results.

Nontrivial Solutions of Systems of Hammerstein Integral Equations with First Derivative Dependence

Infante, Gennaro
;
2017

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 to illustrate the applicability of the theoretical results.
Nontrivial solutions, derivative dependence, fixed point index, cone
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/265383
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