Geodesic
Perturbed Hammerstein integral inclusions with solutions that change sign
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 591-605

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We establish new existence results for nontrivial solutions of some integral inclusions of Hammerstein type, that are perturbed with an affine functional. In order to use a theory of fixed point index for multivalued mappings, we work in a cone of continuous functions that are positive on a suitable subinterval of $[0,1]$. We also discuss the optimality of some constants that occur in our theory. We improve, complement and extend previous results in the literature.
Classification : 34A60, 34B10, 45G10, 47H04, 47H10, 47H30
Keywords: fixed point index; cone; nontrivial solution 
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     author = {Infante, Gennaro and Pietramala, Paolamaria},
     title = {Perturbed {Hammerstein} integral inclusions with solutions that change sign},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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     publisher = {mathdoc},
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     number = {4},
     year = {2009},
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     zbl = {1212.45009},
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Infante, Gennaro; Pietramala, Paolamaria. Perturbed Hammerstein integral inclusions with solutions that change sign. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 4, pp. 591-605. http://geodesic.mathdoc.fr/item/CMUC_2009__50_4_a8/