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
Mathematics Subject Classification
Primary 45G15 Secondary 34B10 34B18 47H30
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G. Infante was partially supported by G.N.A.M.P.A.—INdAM (Italy). F. Minhós was supported by National Funds through FCT-Fundação para a Ciência e a Tecnologia, project SFRH/BSAB/114246/2016. This manuscript was partially written during the authors’ visits in the reciprocal institutions. G. Infante would like to thank the people of the Departamento de Matemática of the Universidade de Évora for their kind hospitality and financial support.
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