Displaying similar documents to “A functional integral inclusion involving Carathéodories.”

Perturbed Hammerstein integral inclusions with solutions that change sign

Gennaro Infante, Paolamaria Pietramala (2009)

Commentationes Mathematicae Universitatis Carolinae

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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.

On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions

S. Carl, S. Heikkilä (1999)

Annales Polonici Mathematici

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We consider the existence of extremal solutions to second order discontinuous implicit ordinary differential equations with discontinuous implicit boundary conditions in ordered Banach spaces. We also study the dependence of these solutions on the data, and cases when the extremal solutions are obtained as limits of successive approximations. Examples are given to demonstrate the applicability of the method developed in this paper.